Application of Information Theory to Study Wood Photodegradation

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Korang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6305182/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Wood is a structured biomaterial able to interact with its environment. An information theoretic framework has been used to model the processing of the environmental inputs to produce output (discoloration) in a photodegradation process. The task of the wood is to receive signals from source with its molecular structure, lignin, acting as the sensor, process them to produce output, blocking “irrelevant” information, coordinating the activities of the internal processing. Maximum temperature (heat) was found to be the most informationally rich environmental input affecting discoloration whereas the wood dedicated a large amount of information to the activities of total rainfall (moisture). The wood blocked greatest amount of information of the sent information by maximum temperature. If the intensity of photodegradation is to be reduced, the wood must be protected from maximum temperature (heat) and moisture. When viewed from this perspective, the active and intelligence nature of wood is reinforced. Complexity Entropy Information Theory Material transformation Mutual information Order Randomness Photodegradation Figures Figure 1 Introduction Natural weathering is a process that changes the appearance of wood over time due to environmental factors mainly driven by lignin degradation. The information about the wood color is degraded or lost after it has been subjected to the environment. These environmental factors that contribute the loss of information can be seen as information destroying factors and as such weathering resonates with information destroying process. This process can be thought of as an information transmission system, with the wood as a channel receiving a vector input from its environment then giving out discoloration as output (Fig. 1 ). The wood processes the received information by separation of molecules. However, this process is complex and influenced by various random elements, such as the internal state of the wood (non-homogeneous and random characteristics), system dynamics, forcing functions (natural variable conditions that occur during the year from one location to another), and initial and boundary conditions (for example, starting material color). Weathering factors fluctuations can be interpreted as self-disclosing messages, conveying information about the system’s state to receptive elements within the system. These uncertainties require a stochastic description of the process, rather than a deterministic one. Information theory can be used to quantify this random and complex process and make statements about the amount of disordering necessary for the loss of the aesthetic function in wood. Well-established metrics in information theory can serve as excellent tools for understanding the dynamics of weathering. For example, wood, as an intelligent biomaterial can assimilate information from its surroundings, responding with changes in structure and properties (Okuma 1998 ). Mutual information then becomes an important metric influencing the ability of wood to endure and adapt to the complexity of the external conditions. The underlying principle for defining such a metric is to assess whether the weathering process can produce an output (discoloration) that meets the variety of the input part as closely as possible. In other words, the output is limited by the extent to which input information has been utilized appropriately. In this study, we will explore the photodegradation of wood using information theory, taking into account the stochastic nature of the wood-environmental interaction and the uncertainties introduced by various random elements. Information theory deals only with the statistics, and not the meaning of the messages sent and received. The aim of this study is to develop a better understanding of the complex process of weathering and to make quantitative statements about the amount of disordering necessary for the loss of aesthetic function in wood. In particular, we want to know how much information is gained about wood colour at a future time based on the conditional probability of occurrence of the environmental/input conditions. We want to quantify the amount of disordering needed to reduce the aesthetic value of wood due to environmental inputs. In order to develop effective methods to avoid weather-induced deterioration, it is important to quantitatively assess how well a wood can handle the complexity induced by the environmental inputs. When considering wood weathering as a system, it is essential to reveal the laws of information governing such a system which is fundamental to knowledge management. Materials and methods Wood Samples and weathering site In this study, 10 samples were prepared from Piptadeniastrum africanum (Hook.f.) Brenan. Each sample, with dimensions of 10 (Length) \(\:\times\:\) 4 (Width) \(\:\times\:\) 2 (Thickness) cm 3 , was cut to expose the longitudinal radial surface for degradation analysis, ensuring that all samples were free of any discoloration and other defects. The moisture content of the specimens before weathering was about 12%. The samples were exposed at 0° angle (horizontally), facing south. The 0° angle was selected for the experiment as it has been shown by Davis and Sims ( 1983 ) to maximize the ultraviolet light intensity by over 10%. The natural weathering test was conducted on the samples at Faculty of Renewable Natural Resources, Kwame Nkrumah University of Science and Technology (Ghana, latitude 6°40′35.904″ longitude − 1°33′52.362″, elevation 268 m), between February 2024 and May 2024 (i.e., approximately 122 days). It is thought that Kumasi receives higher solar radiation during this time period as per Odoi-Yorke et al ( 2023 ). The samples were exposed on a rooftop, free from any obstacles that could block sunlight and other climatic factors, during the outdoor exposure. According to Schnabel et al ( 2009 ), who cite Reiter et al ( 1972 ), an increase in elevation is associated with a rise in UV light intensity. Environmental inputs such as temperature, relative humidity, sunshine duration, precipitation, and solar radiation on a horizontal plane were measured on site. Solar radiation is assumed to be the ultimate driver of color changes and surface degradation of the wood samples. Solar radiation data was obtained from a solar radiation database (SoDA). Color measurement Color change caused by natural weathering was evaluated with the help of smartphone (iPhone 13, Apple Inc.) every week. Images were taken after allowing the samples to cool at room temperature and further processed using ImageJ and TRIGIT, a web-based application (Tjandra et al 2023 ). TRIGIT recorded the average L* , a* , and b* color values, obtained from four readings or quadrants, for the region of interest from the exposed surface. Additional color measurements from ImageJ showed that TRIGIT produced equally reliable results. The color changes were determined by referring to the coordinates using the Commission International de l’Eclairage (CIE) L*a*b* color space (abbreviated CIELAB) in which L* denotes lightness or brightness (black to white), and a* and b* denote redness (green to red) and yellowness (blue to yellow), respectively. L* describe the achromatic axis while a* and b* describe the chromatic coordinates. This system is the most common method for estimating the color of a material. The change in color ( \(\:{\varDelta\:E}_{ab}^{*})\) of each sample was calculated by determining the Euclidean distance between two colors as: $$\:{\varDelta\:E}_{ab}^{*}=\:\sqrt{{(\varDelta\:{L}^{*})}^{2}+\:{(\varDelta\:{a}^{*})}^{2}+{(\varDelta\:{b}^{*})}^{2}}$$ 1 where \(\:{\varDelta\:E}_{ab}^{*}\) is the wood color change due to weathering, \(\:\varDelta\:{L}^{*}\) , \(\:\varDelta\:{a}^{*}\) and \(\:\varDelta\:{b}^{*}\) values are the color differences and were calculated from measurements made before and after each weathering period. By summing up \(\:{\varDelta\:E}_{ab}^{*}\) for all analyzed points in time, the course of the color changes can be taken into account: $$\:\sum\:_{i-\text{1,1}}^{n}{\varDelta\:E}_{1,n}^{*}=\:{\varDelta\:E}_{\text{0,1}}+\:{\varDelta\:E}_{\text{1,2}}+\dots\:+\:{\varDelta\:E}_{n-1,\:n}$$ 2 Chroma is defined as the Euclidean distance between a color and its achromatic point of the same lightness: $$\:{C}^{*\:}=\:\sqrt{{a}^{*2}+{b}^{*2}}$$ 3 In all cases the overall average of 10 samples were used for comparison before and after the specific exposure times. Shannon measure of information (Entropy) To assess the transformation of wood surfaces (i.e., change of state) caused by weathering we chose a micro-perspective approach, concerned with the fate of particular components of the system. Photodegradation is a problem with uncertainty since we do not know a priori the outcome of this process. It introduces randomness to the wood structure leading to unpredictability, thus increasing uncertainty (entropy). The central idea of information theory is to offer a quantitative measure of uncertainty. Uncertainty is linked to the potential occurrence of ensemble of states; its magnitude depends on the number of possible states and the probabilities associated with each state. The more likely one of these states, the less able is the system to convey further information. Shannon ( 1948 ) selected a straightforward logarithmic measure to define the uncertainty associated with the occurrence of the following possible states: $$\:H=\sum\:_{\text{i}=1}^{\text{n}}{\text{p}}_{\text{i}}\text{log}\left(\frac{1}{{\text{p}}_{\text{i}}}\right)\:$$ 4 where, H represents the Shannon measure of information and p i are the probabilities of each of the n possible states, here normalized values of the factors (where, \(\:\sum\:_{\text{i}=1}^{\text{n}}{\text{p}}_{\text{i}\:}=1;\:\) the probabilities of all possible events must sum up to unity). It has the maximum value of log( N ) when all possible states (normalized values) are equally probable. Before quantifying information, normalization of both input (environmental inputs) and output (total color change) data occurred, scaling them within the specified range [0 to 1]. This normalization was conducted using Eq. 5: $$\:\frac{({\text{x}}_{\text{i}}-{\text{x}}_{\text{m}\text{i}\text{n})}}{{(\text{x}}_{\text{m}\text{a}\text{x}}-\:{\text{x}}_{\text{m}\text{i}\text{n})}}$$ where, \(\:{\text{x}}_{\text{i}}\) , \(\:{\text{x}}_{\text{m}\text{i}\text{n}}\) , \(\:{\text{x}}_{\text{m}\text{a}\text{x}}\) represent the original, minimum and maximum values of both the input and output variables being normalized. The joint entropy H ( I , O ) is defined as: $$\:H\left(I,O\right)=\:-\sum\:_{\text{i}=1}^{\text{i}}\sum\:_{\text{J}=1}^{\text{o}}\text{p}\left({\text{I}}_{\text{i}},{\text{O}}_{\text{j}}\right)\text{l}\text{o}\text{g}\text{p}({\text{I}}_{\text{i}},{\text{O}}_{\text{j}})$$ 6 Here, \(\:\text{p}\left({\text{I}}_{\text{i}},{\text{O}}_{\text{j}}\right)\) denotes the joint probability that input ( I ) is in state \(\:{I}_{\text{i}}\) and output ( O ) is in state \(\:{O}_{\text{j}}\) . The number of possible states, \(\:i\:\) and \(\:o\) , may not be the same. The central information-theoretical quantity describing the reduction of uncertainty, the information content (transinformation), can be obtained via two routes: first, considering the input entropy H ( I ) (dependent solely on the environmental variable or weathering factors) and the output entropy H ( O ) (dependent solely on the discoloration). If there exists some level of dependence between input weathering factors and output state, both entropies overlap to a certain degree, and their joint entropy H ( I , O ) will be lesser than the sum of both entropies. The amount of overlap is the transinformation T : T = H ( I ) + H ( O ) – H ( I , O ). The difference H ( I ) – T ( I ; O ) is termed equivocation entropy H ( I | O ), signifying the uncertainty about the input after knowing the output. Similarly, the difference H ( O ) – T ( I ; O ) is labeled ambiguity entropy H ( O | I ), representing the uncertainty about the discoloration when an input is provided. Logarithms were taken to the base 10. For a detailed derivation we refer to Jones and Jones ( 2000 ). Analyses were performed using Microsoft Excel software (version 16.87). Results (Photodegradation) Table 1 Wood color changes after 18 weeks of weathering L* a* b* Reference state 43.15 15.23 27.56 After 18 weeks of weathering 66.42 1.90 5.25 In relation to the reference state, P. africanum wood has a low lightness level, as defined by Nishino et al (1998). However, it also exhibits a tendency to move towards the b* axis, which is indicative of lighter wood. With natural weathering, the L* value, measuring lightness, exhibited a rise temporally, with a 53% increase rate. The initial darkening phase ended after the first 1.5 weeks, followed by a gradual graying of the samples. The chromatic values ( a* and b* ) decreased over time, approaching zero, indicating that the samples were becoming increasingly achromatic (gray). A graph of the chroma ( C* ) and L* values revealed a more pronounced change after the 10th week, with an increase in lightness and a decrease in chroma (data not shown). After the first week, the total color change ( \(\:{\varDelta\:E}_{ab}^{*})\) was measured at 3.35, which was noticeable at that time. However, the transformation was not yet complete, and by the 18th week, the total color change had increased significantly to 34.89, resulting in a completely new color. The observed changes in wood color, specifically the increase in lightness and decrease in chromatic values, support the assumption that wood color serves as an indicator of disorganization. Table 2 Change in entropy before and after weathering of color parameters L* a* b* Reference state 0.7365 0.8194 0.7967 After 18 weeks of weathering 0.7592 0.7967 0.7967 The degradation of molecules controlling lightness ( L* ) is fast (increasing entropy at the end of exposure period (18 weeks)), whereas the degradation of molecules controlling a * and b * coordinates are rather slow in P. africanum . This is analogous to the tendency for stored information about lightness to diminish (initial darkening, then graying). Information initially certain about L* tends to become uncertain introducing randomness in the lightness of the wood surface thereby resulting in greater effective variability of the exposed wood surfaces. Further chemical analysis is needed to uncover the details of the chemical changes. What we do not know for now is when the entropy reaches its maximum (i.e., completely disorganized or no further disorganization can occur) as biological phenomena have directionality with time (Aoki 1995 ). However, quantitatively the amount of disordering necessary for the loss of darker tone of P. africanum is 0.0227 after 18 weeks of natural weathering. Table 3 Joint entropies Weathering factor Output factor Joint entropy Solar irradiance 𝛥E* ab 1.1831 Ave. Rainfall 𝛥E* ab 1.1710 Min. Temperature 𝛥E* ab 1.1212 Max. Temperature 𝛥E* ab 1.1840 Ave. Temperature 𝛥E* ab 1.1672 Relative Humidity, 9 am 𝛥E* ab 1.1434 Relative Humidity, 3 pm 𝛥E* ab 1.1497 Sunshine duration 𝛥E* ab 1.1774 Total Rainfall 𝛥E* ab 1.1066 Joint entropy is a measure of the uncertainty associated with a set of variables (a two-part system). In other words, it represents the total amount of information one has when both input information and output information are known. As the total information in a system, it is the sum of the mutual information, ambiguity, and equivocation. The higher the joint entropy, the greater the degree of disorder or randomness between the two variables. Maximum temperature had the highest joint entropy with total color change whereas total rainfall had the least joint entropy with total color change. From the joint entropy, we can anticipate that maximum temperature may have significant impact on the photodegradation process in P. africanum . Table 4 Marginal entropies of the input and output factors Weathering factors Entropy Average Rainfall 0.7491 Max. Temperature 0.8829 Relative Humidity, 9 am 0.8017 Sunshine Duration 0.8829 Solar Irradiance 0.8813 Ave. Temperature 0.8495 Relative Humidity, 3 pm 0.8144 Min. Temperature 0.7573 Total Rainfall 0.7283 Total Color Change 0.8829 Table 4 gives the summary of marginal entropies of total color change and the weathering factors. These weathering factors are assumed to be information destroyers introducing randomness in the wood surface. They cause stored information to diminish. Marginal entropies are indices of complexity of the factors that are perceived as being most critical for the photodegradation process. It measures nondeterministic or unpredictable behavior of the variables studied. Total rainfall had the minimum entropy, implying a marginally reduced level of uncertainty ( low complexity ). There is an elevated level of certainty or confidence in predicting the outcome of total rainfall record or it is more likely to be a particular state. In contrast, total color change, average rainfall, maximum temperature, relative humidity at 9 am, and sunshine duration exhibited the highest entropies ( high complexity ). From micro-perspective, these variables can be found in different states (or different arrangements of individual states) and thus the more able are they to convey further information. High information of a single factor means that the amount of novelty in that factor (message) is large and, therefore, that uncertainty predominates. The values describe the complexity of the random variable and the amount of hidden or missing information required on average to describe them. For example, one would need an average information of size 0.8829 to describe total color change fully. The average entropy of all the considered weathering factors was 0.8403. Interestingly, the amount of information contained in the output was equal to the information contained in the inputs with highest marginal entropy (0.8829). Expectedly, the contribution of the input information to the output information was not more than the amount of input information. Table 5 Mutual information between environmental variables and total color change Weathering factors Output Factor Mutual Information Max. Temperature 𝛥E* ab 0.5818 Solar Irradiance 𝛥E* ab 0.5811 Sunshine Duration 𝛥E* ab 0.5753 Average Temperature 𝛥E* ab 0.5652 Relative Humidity, 3pm 𝛥E* ab 0.5476 Relative Humidity, 9am 𝛥E* ab 0.5412 Min. Temperature 𝛥E* ab 0.5190 Average Rainfall 𝛥E* ab 0.5149 Total Rainfall 𝛥E* ab 0.5046 Mutual information, also known as transinformation, is interpreted as the average information received by the output transmitted by the input. It gives a measure to the transmitted information between the input and output in a system. In simple terms, it is the decrease in uncertainty (or the gain in certainty) about the output (i.e., discoloration) that is derived from observing a weathering factor. It is the input flow which affects output, representing the strength of the relationship or association between the two random variables. From cybernetics and systems viewpoint, this term is a measure of the degree to which the color of wood samples takes actions coordinated with their immediate surrounding. It is usually referred to as transmission in information theory, measuring the internal constraints in a communication system. It quantifies the degree to which knowledge about the values of one variable diminishes our uncertainty in predicting the values of the other variable. Maximum temperature is informationally rich variable in explaining total color change. Total rainfall gives the least information with total color change. The weathering factors studied communicate some information about wood color; the average amount communicated is 0.5479. The non-zero mutual information implies that wood is not independent of its environment and provides a limit to cope. The wood apparently would be receiving the environmental messages with only about an average of 67% efficiency. Table 6 Conditional entropies (equivocation and ambiguity) Weathering factors Output Equivocation Ambiguity Solar Irradiance 𝛥E* ab 0.3002 0.3018 Average Rainfall 𝛥E* ab 0.2342 0.3680 Min. Temperature 𝛥E* ab 0.2383 0.3634 Max. Temperature 𝛥E* ab 0.3011 0.3011 Average Temperature 𝛥E* ab 0.2843 0.3177 Relative Humidity, 9 am 𝛥E* ab 0.2605 0.3417 Relative Humidity, 3 pm 𝛥E* ab 0.2668 0.3353 Sunshine Duration 𝛥E* ab 0.2945 0.3076 Total Rainfall 𝛥E* ab 0.2237 0.3783 Table 6 gives a summary of the conditional entropies between the input and output factors. Equivocation measures the uncertainty in the input given the output variable while ambiguity gives the uncertainty in the output given the input variable. From the standpoint of data analysis, equivocation can be considered as a measure of irrelevance of the weathering factors with respect to total color change. Ambiguity averaged 0.3350 with equivocation averaging 0.2671 for all weathering factors. The wood material dedicates relatively higher amount of information to proper functioning of the weathering activity than blocking or discarding the sent environmental information. This can be explained by the fact that wood was not treated to withstand weathering. Alternatively, it is the amount of information generated within the wood block itself and at least not related to the known input is relatively higher than the amount of input information the wood blocks. In other words, higher components of the output (discoloration) are autonomously produced and are unrelated to weathering inputs. One would need a little more information to clarify any input variable if given the color change knowledge than the other way round. Total rainfall recorded the greatest equivocation with minimum temperature the largest ambiguity. Equivocation from cybernetics viewpoint (Conant 1976 ) can be viewed as input flow that is blocked or rejected by the wood whereas ambiguity is the flow internal to the system dedicated to coordinating the degradation process akin to computation (i.e., computation - selection of particular chemical bonds to break upon receiving ultimate information from the sun ). Ambiguity can therefore be referred to as the photodegradation process uncertainty. The blockage of information is an important function of information-processing (smart) materials. They filter the information received from their environment, allowing only the “relevant” aspects to affect their output. Ambiguity is the amount of uncertainty per step about color change, given complete knowledge of weathering input. It corresponds to internally-generated information i.e., autonomous behavior, since it corresponds to behavior which has no apparent cause (at least not in the known environmental influences). It can be viewed as noise analogous to that on a communication channel – a message at the output not caused by a message at the input. It interferes with good communication. With ambiguity and equivocation being non-zero means that even if one has complete knowledge of the weathering factors, there is still residual uncertainty about the weathering output, i.e., state of discoloration . Also, the “channel” which links the wood to its environment is a noisy one. These values can be used to measure the performance of a particular wood species resistance to photodegradation. For example, wood with high resistance to weather and UV radiation would have a higher equivocation and lower ambiguity. In other words, the wood would be able to reduce internal coordination to the minimum as soon as possible and block or reject most of UV and visible light radiation (controlled equivocation). Another pathway would be to perform as little blockage as possible by avoiding irrelevant components of the environmental factors. Discussion Darkening and Graying Weathering generally induces a rapid darkening of wood surfaces because of the degradation of lignin and extractives into quinones (darker in color), which are progressively washed out leaving the cellulose-rich wood surface lighter in color as the process progresses. Interpretation of the model The model presented in this paper may be interpreted in several ways. First, as a method of description, and one particularly suited to complex, active communication. Second, the model makes predictions about photodegradation of wood surfaces, the accuracy of which will depend upon the adequacy of our sample, and the consistency of the discoloration process. In addition, the probability model could be used to simulate photodegradation process, generating records of discoloration sequences that would be difficult to distinguish from real records. Indeed, this similarity is an indication of the adequacy of the model. Marginal Entropies The information measured in Shannon’s theory is limited to the syntactic level, focusing on the statistical and structural properties of the signal. What the study has done here is to model a weathering system int terms of input-output relationship using communication system and cybernetics frameworks. The approach has not only revealed the information dynamics and architecture but also quantified the amount of information stored between the input and output and components transmitted within the system. Entropy as a coarse grain property allows us to measure the uncertainty about what happens microscopically or scales many orders of magnitude smaller than the observation scale (Crevecoeur 2019 ). Thus, the discoloration was more random resulting from the breaking down of highly organized molecules or simply rearrangement of the molecules inside the wood (Jordan 2022 ). Transmission or transinformation Transinformation is the key metric for evaluating and comparing the significance of different weathering factors on discoloration of wood surfaces. It is the amount of information transmitted between the two variables. Mutual information, a measure of relatedness between the input and output variables, accounts for the usefulness in systems science. It reveals hidden relationships and dependencies that do not manifest themselves in the covariance or linear correlation coefficient (Kraskov et al. 2004 ), a kind of generalized correlation. It is a measure of control power as per Bialek ( 2024 ). It is observed with different names; e.g., “ predictive information ”, “ stored information ”, “ effective measure complexity ” (Shalizi and Crutchfield (2001); Bialek et al. ( 2001 ); Bialek and Tishby ( 1999 ); Arnold ( 1996 ). As a measure of complexity, it characterizes order-to-disorder phase transition in the transformation process. This measure will be referred to as photodegradation/deteriorative complexity giving the amount of sensitivity of the wood to weathering factors. It represents the amount of information needed to fully characterize the initial (starting material) and final states of the wood color (Ruth and Bullard, 1993 ). A completely reversible process indicates perfect information transmission, whereas any deviation from this ideal situation emphasizes the irreversible nature of the photodegradation process. This is because the color after 18 weeks of weathering resulted in a completely new color as formation of new chemical compounds or structures are different from the original state. A high mutual information indicates a strong correlation between random variables. Specifically, it was observed that the maximum temperature “communicated” largest information about discoloration, while the total rainfall had the least effect. Changes in the maximum temperature are more likely to result in noticeable changes in the discoloration, while changes in the total rainfall are less predictive of the discoloration. The higher value for information transmission for maximum temperature may be the result of adaptation to photochemical reactions during harsh interactions. Elevated temperature generates higher vibration energy; thus, photons can split chemical bonds more easily than at ambient temperatures (Preklet et al. 2018 ). In the weathering process, elevated temperature can lead to increased photodegradation, as the higher vibration energy makes it easier for photons to break chemical bonds in the wood material. Alternatively, it could imply that the wood has a greater solar irradiation sensitivity at elevated temperatures or possibly energy transfer is reduced at low temperatures. It has been suggested that heat and irradiation may in some way complement each other and that heat exposure alone can cause reactions comparable to UV exposure (Yatagai and Zeronian 1994 ). Solar irradiation was the second most informationally rich variable explaining discoloration. It was only lesser by 0.0007 compared to maximum temperature. According to Platzman and Franck ( 1956 ), the absorption of ultraviolet light does not itself break bonds. The initial acts energy transfer are all ones in which energy is communicated to the electronic systems of molecules; subsequent rearrangement of atomic positions may then result in dissociation. It replaces the notion that solar irradiation acts merely by breaking chemical bonds directly. Solar irradiation and heat provide more or less random methods of disordering the wood biochemical structure. Finally, the apparent activation energies for the L* was positive while negative for a* and b* , indicating that the reaction decreases slowly with increasing temperature (data not shown). The molecules controlling the brightness are most sensitive to thermal agitations. Conditional entropies The concepts of equivocation and ambiguity, as outlined in the cybernetics framework (Conant 1974 , 1976 ), provide valuable insights into the weathering performance of wood materials. In this study, we have demonstrated how these principles can be applied to understand and predict the degradation of wood exposed to various weathering factors (entropy injectors). Equivocation, defined as the ability of the wood to block or reject certain environmental inputs, was found to be a critical factor in determining the resistance of wood to weathering. It defines the control and regulatory mechanisms of the wood to photodegradation process. Our results show that the wood is able to block or reject a greater amount of information from maximum temperature with solar irradiation as second. The wood, however, either blocks or filters out least amount of information flow from total rainfall. The higher the value of the equivocation, the more input messages must be transmitted and recognized by the wood. Solar irradiation presents more information than needed for chemical cleaving. The wood then blocks as much as possible because the wood is mainly responsive to UV component and some visible light of sunlight. The ability of the wood samples to reject or block some of environmental information packet implies that they exhibit adaptive behavior. Ambiguity, on the other hand, represents the wood’s internal computational or processing capabilities that govern its response to weathering factors. Moisture carries stepwise instruction that specifies photodegradation process that transforms the wood colour. According to Eder et al. ( 2021 ), ambiguity is the intrinsic “code” or algorithm that determines how the material responds to external stimuli, processes information, and adapts to changing conditions. Moreover, it codes the operation, acting as a sensor for transforming a particular environmental input into output actions. The wood possesses the ability to internally regulate its moisture content in response to fluctuations in relative humidity and temperature. For instance, in our study, the initial moisture content of the wood specimens, starting at 12%, rose to approximately 16% by the end of the exposure period. The internal flow can be linked to a computational activity, where the wood selects which particular chemical bonds to cleave upon receiving “ultimate” information from the sun’s radiation or heat. For complex tasks, the wood would require a lot of internal coordination or calculation that is reflected by the ambiguity. It was found that the specimens required a lot of information coordinating the input flow from total rainfall (i.e., moisture), implying the complexity of the interaction, and thus reducing the mutual information. In contrast, maximum temperature required a smaller amount of information to internally coordinate the information flow and hence high throughput (mutual information). The interaction of wood structure and maximum temperature can therefore be seen as a simple task. Wood is not passively undergoing photodegradation, but is actively “computing” or processing environmental inputs and orchestrating a specific response in the form of selective bond cleavage and other chemical changes, resulting in the discoloration at the macro state. It is widely believed that intrinsic activity in wood is triggered by the dynamic activity of water as highlighted by Eder et al. ( 2021 ). The transformations induced by water inside the wood serve as the fundamental link between matter and energy. Water replaces functions of electricity in natural materials like wood, acting as a vital interface in the photodegradation process and the hydroxyl groups from lignin, hemicelluloses and cellulose play a key role in this process. This explains how water can wash away fragmented lignin and hemicellulose, as noted by Evans et al. (2015). Furthermore, water enhances light penetration into previously inaccessible areas, effectively opening up new pathways for light to react and interact with the wood, a phenomenon discussed by Feist and Hon ( 1984 ). The wood dedicating a larger amount of information to the activity of water implies the cell wall is more hydrophilic rendering the wood more prone to water sorption. Water then completely breaks hydrogen bonds in the amorphous part of the wood. As the photodegradation process progresses, the wood undergoes cycles of water uptake and loss resulting in visible swelling and shrinking. From a cybernetics viewpoint, wood as an active biological material can thus be considered as a machine – molecular one (Bensaude-Vincent 2011 ; Eder et al. 2021 ). The question that arises is whether there are optimal values for transinformation, equivocation, and ambiguity. An optimized system, as defined by Jantsch ( 1980 ), should maintain a balance of approximately 50% equivocation and ambiguity and 50% confirmation (transinformation). This balance suggests that the system is functioning efficiently and effectively, with a sufficient level of uncertainty and novelty to support learning and adaptation, while also providing enough structure and predictability to enable successful communication and coordination. These findings have important implications for design and development of more sustainable wood-based materials. There are some limitations in the methods used in this study that should be noted. There are several weathering factors which have not been considered here. First, no information has been made for chemistry of wood and air quality for example. Secondly, it was not possible to interpret discoloration which could possibly have a function in “metacommunication”, i.e., communication that affects the interpretation of other communication. Even with these limitations, however, the statistical method undertaken is a powerful tool for analyzing communications systems and weathering systems. It demonstrates, first, that communication is occurring between the wood and its environmental variables. Actual changes in wood colour do occur following the execution of specific acts by environmental variables. Conclusion This study demonstrates how the concepts of random variables and probability distributions can be applied to uncover the mathematical framework underlying complex physical processes, such as photodegradation. By modelling the inherent effective variability and uncertainty in environmental factors and material responses, we provide a quantitative foundation for predicting degradation outcomes and understanding the mechanisms driving these changes. Our findings indicate that specific environmental factors – such as moisture, solar irradiation and maximum temperature – play crucial roles in influencing wood discoloration. Notably, we identified the signals that convey the most information regarding these changes, providing insights into the dynamics of wood discoloration. Declarations Disclosure statement No potential conflict of interest was reported by the authors. References Aoki I (1995) Entropy production in living systems: from organisms to ecosystems. Thermochimica Acta 250:359–370. Arnold DV (1996) Information-theoretic analysis of phase transitions. Complex Systems 10:143–155. Bensaude-Vincent B (2011) Materials as machines. In: Carrier M, Nordmann A (eds) Science in the Context of Applications. Boston Studies in the Philosophy of Science, vol 274. Springer, Dordretcht. Bialek W (2024) Ambitions for theory in the physics of life. SciPost Physics Lecture Notes. arXiv:2401.15538v1. Bialek W, Nemenman I, Tishby N (2001) Predictability, complexity and learning. arXiv:physics/0007070v3. Bialek W, Tishby N (1999) Predictive information, E-print, arxiv.org, cond-mat/9902341. Crevecoeur GU (2019) Entropy growth and information gain in operating organized systems. AIP Advances 9, 125041. Conant RC (1974) Information flows in hierarchical systems. International Journal of General Systems 1:1, 9–18. Conant RC (1976) Laws of information which govern systems. IEEE Transactions on Systems, Man, and Cybernetics 6(4). Davis A, Sims D (1983) Weathering of polymers. Elsevier Applied Science Publishers. Eder M, Schäffner W, Burgert I, Fratzl P (2021) Wood and the activity of dead tissue. Adv. Mater. 33:2001412. Evans P, Chowdhury MJ, Mathews B, Schmalzl S, Ayer S, Kiguchi M, Kataoka Y (2005) Weathering and surface protection of wood. In Kutz M (ed) Handbook of Environmental Degradation of Materials. William Andrew Publishing, Norwich NY. Feist WC, Hon DNS (1984) Chemistry of weathering and protection. In Rowell RM (ed) Chemistry of Solid Wood. American Chemistry Society, Washington DC. Jantsch E (1980) The Self-Organizing Universe, Pergamon Press, Oxford. Jones GA, Jones JM (2000) Information and Coding Theory. Springer-Verlag, London. Jordan CF (2022) Evolution from a Thermodynamic Perspective: Implications for Species Conservation and Agricultural Sustainability. Springer Nature AG, Switzerland. Kraskov A, Stögbauer H, Grassberger P (2004) Estimating mutual information. Physical Review E 69:066138. Odoi-Yorke F, Akpahou R, Opoku R, Mensah LD (2023) Technical, financial, and emissions analyses of solar water heating systems for supplying sustainable energy for hotels in Ghana. Solar Compass 7:100051. Okuma M (1998) Wood utilization in the 21 st century. Wood Industry 52:98–103. Preklet E, Tolvaj L, Bejo L, Varga D (2018) Temperature dependence of wood photodegradation. Part 2: evaluation by Arrhenius law. J. Photochem. Photobiol. A: Chem. 356:329–333. Platzman RL, Franck J (1956) A physical mechanism for the inactivation of proteins by ionizing radiation. In Yockey HP, Platzman RL, Quastler H (eds) Symposium on Information Theory in Biology. Pergamon Press, New York, London, Paris, Los Angeles. Reiter R, Carnuth W, Sládkoviè R (1972) Ultraviolettstrahlung in alpinen Höhenlagen. Wetter Leben 24:231–347. Ruth M, Bullard CW (1993) Information, production and utility. Energy Policy 21:1059–1067. Schnabel T, Zimmer B, Petutschnigg AJ (2009) On the modelling of colour changes of wood surfaces. Eur. J. Wood Prod. 67:141–149. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:389–423. Shalizi CR, Crrutchfield JP (2001) Computational mechanics: pattern and prediction, structure and simplicity. Journal of Statistical Physics 104(3/4):817–879. Tjandra AD, Heywood T, Chandrawati R (2023) Trigit: a free web application for rapid colorimetric analysis of images. Biosensors and Bioelectronics: X 14:100361. Yatagai M, Zeronian SH (1994) Effect of ultraviolet light and heat on the properties of cotton cellulose. Cellulose 1:205–214. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6305182","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":443797656,"identity":"98431590-b43a-43e9-adb9-0ed1b7ce17b3","order_by":0,"name":"Jerry Oppong Adutwum","email":"data:image/png;base64,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","orcid":"","institution":"Council for Scientific and Industrial Research – Forestry Research Institute of Ghana","correspondingAuthor":true,"prefix":"","firstName":"Jerry","middleName":"Oppong","lastName":"Adutwum","suffix":""},{"id":443797657,"identity":"428e9ecf-8f69-42fe-8c60-71fe382d5310","order_by":1,"name":"Peniel Adjei","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Peniel","middleName":"","lastName":"Adjei","suffix":""},{"id":443797658,"identity":"51e65900-84df-43b8-aecb-0f8383f67d2c","order_by":2,"name":"Francis Wilson Owusu","email":"","orcid":"","institution":"Council for Scientific and Industrial Research – Forestry Research Institute of Ghana","correspondingAuthor":false,"prefix":"","firstName":"Francis","middleName":"Wilson","lastName":"Owusu","suffix":""},{"id":443797659,"identity":"cbc7d445-3270-4095-a707-2a1e64820287","order_by":3,"name":"James K. Korang","email":"","orcid":"","institution":"Council for Scientific and Industrial Research – Forestry Research Institute of Ghana","correspondingAuthor":false,"prefix":"","firstName":"James","middleName":"K.","lastName":"Korang","suffix":""}],"badges":[],"createdAt":"2025-03-25 15:23:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6305182/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6305182/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81132053,"identity":"cd782c0a-6f62-46b7-94a6-8d9fb0acb7fc","added_by":"auto","created_at":"2025-04-22 14:51:58","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":331005,"visible":true,"origin":"","legend":"\u003cp\u003eThe weathering model\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6305182/v1/3df70f7939130280da0e98f8.png"},{"id":81991082,"identity":"f0975c56-78b8-4ed2-a19e-d524b4e6b520","added_by":"auto","created_at":"2025-05-05 16:38:38","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1057113,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6305182/v1/1db5075c-3ecb-4125-9f59-31abb97237ed.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Application of Information Theory to Study Wood Photodegradation","fulltext":[{"header":"Introduction","content":"\u003cp\u003eNatural weathering is a process that changes the appearance of wood over time due to environmental factors mainly driven by lignin degradation. The information about the wood color is degraded or lost after it has been subjected to the environment. These environmental factors that contribute the loss of information can be seen as information destroying factors and as such weathering resonates with information destroying process. This process can be thought of as an information transmission system, with the wood as a channel receiving a vector input from its environment then giving out discoloration as output (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The wood processes the received information by separation of molecules. However, this process is complex and influenced by various random elements, such as the internal state of the wood (non-homogeneous and random characteristics), system dynamics, forcing functions (natural variable conditions that occur during the year from one location to another), and initial and boundary conditions (for example, starting material color). Weathering factors fluctuations can be interpreted as self-disclosing messages, conveying information about the system\u0026rsquo;s state to receptive elements within the system. These uncertainties require a stochastic description of the process, rather than a deterministic one. Information theory can be used to quantify this random and complex process and make statements about the amount of disordering necessary for the loss of the aesthetic function in wood. Well-established metrics in information theory can serve as excellent tools for understanding the dynamics of weathering. For example, wood, as an intelligent biomaterial can assimilate information from its surroundings, responding with changes in structure and properties (Okuma \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). Mutual information then becomes an important metric influencing the ability of wood to endure and adapt to the complexity of the external conditions. The underlying principle for defining such a metric is to assess whether the weathering process can produce an output (discoloration) that meets the variety of the input part as closely as possible. In other words, the output is limited by the extent to which input information has been utilized appropriately.\u003c/p\u003e \u003cp\u003eIn this study, we will explore the photodegradation of wood using information theory, taking into account the stochastic nature of the wood-environmental interaction and the uncertainties introduced by various random elements. Information theory deals only with the statistics, and not the meaning of the messages sent and received. The aim of this study is to develop a better understanding of the complex process of weathering and to make quantitative statements about the amount of disordering necessary for the loss of aesthetic function in wood. In particular, we want to know how much information is gained about wood colour at a future time based on the conditional probability of occurrence of the environmental/input conditions. We want to quantify the amount of disordering needed to reduce the aesthetic value of wood due to environmental inputs.\u003c/p\u003e \u003cp\u003eIn order to develop effective methods to avoid weather-induced deterioration, it is important to quantitatively assess how well a wood can handle the complexity induced by the environmental inputs. When considering wood weathering as a system, it is essential to reveal the laws of information governing such a system which is fundamental to knowledge management.\u003c/p\u003e"},{"header":"Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eWood Samples and weathering site\u003c/h2\u003e \u003cp\u003eIn this study, 10 samples were prepared from \u003cem\u003ePiptadeniastrum africanum\u003c/em\u003e (Hook.f.) Brenan. Each sample, with dimensions of 10 (Length) \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\times\\:\\)\u003c/span\u003e\u003c/span\u003e 4 (Width) \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\times\\:\\)\u003c/span\u003e\u003c/span\u003e 2 (Thickness) cm\u003csup\u003e3\u003c/sup\u003e, was cut to expose the longitudinal radial surface for degradation analysis, ensuring that all samples were free of any discoloration and other defects. The moisture content of the specimens before weathering was about 12%. The samples were exposed at 0\u0026deg; angle (horizontally), facing south. The 0\u0026deg; angle was selected for the experiment as it has been shown by Davis and Sims (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e1983\u003c/span\u003e) to maximize the ultraviolet light intensity by over 10%. The natural weathering test was conducted on the samples at Faculty of Renewable Natural Resources, Kwame Nkrumah University of Science and Technology (Ghana, latitude 6\u0026deg;40\u0026prime;35.904\u0026Prime; longitude \u0026minus;\u0026thinsp;1\u0026deg;33\u0026prime;52.362\u0026Prime;, elevation 268 m), between February 2024 and May 2024 (i.e., approximately 122 days). It is thought that Kumasi receives higher solar radiation during this time period as per Odoi-Yorke et al (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The samples were exposed on a rooftop, free from any obstacles that could block sunlight and other climatic factors, during the outdoor exposure. According to Schnabel et al (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2009\u003c/span\u003e), who cite Reiter et al (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e1972\u003c/span\u003e), an increase in elevation is associated with a rise in UV light intensity. Environmental inputs such as temperature, relative humidity, sunshine duration, precipitation, and solar radiation on a horizontal plane were measured on site. Solar radiation is assumed to be the ultimate driver of color changes and surface degradation of the wood samples. Solar radiation data was obtained from a solar radiation database (SoDA).\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eColor measurement\u003c/h3\u003e\n\u003cp\u003eColor change caused by natural weathering was evaluated with the help of smartphone (iPhone 13, Apple Inc.) every week. Images were taken after allowing the samples to cool at room temperature and further processed using ImageJ and TRIGIT, a web-based application (Tjandra et al \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). TRIGIT recorded the average \u003cem\u003eL*\u003c/em\u003e, \u003cem\u003ea*\u003c/em\u003e, and \u003cem\u003eb*\u003c/em\u003e color values, obtained from four readings or quadrants, for the region of interest from the exposed surface. Additional color measurements from ImageJ showed that TRIGIT produced equally reliable results. The color changes were determined by referring to the coordinates using the Commission International de l\u0026rsquo;Eclairage (CIE) L*a*b* color space (abbreviated CIELAB) in which \u003cem\u003eL*\u003c/em\u003e denotes lightness or brightness (black to white), and \u003cem\u003ea*\u003c/em\u003e and \u003cem\u003eb*\u003c/em\u003e denote redness (green to red) and yellowness (blue to yellow), respectively. \u003cem\u003eL*\u003c/em\u003e describe the achromatic axis while \u003cem\u003ea*\u003c/em\u003e and \u003cem\u003eb*\u003c/em\u003e describe the chromatic coordinates. This system is the most common method for estimating the color of a material. The change in color (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:E}_{ab}^{*})\\)\u003c/span\u003e\u003c/span\u003e of each sample was calculated by determining the Euclidean distance between two colors as:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{\\varDelta\\:E}_{ab}^{*}=\\:\\sqrt{{(\\varDelta\\:{L}^{*})}^{2}+\\:{(\\varDelta\\:{a}^{*})}^{2}+{(\\varDelta\\:{b}^{*})}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:E}_{ab}^{*}\\)\u003c/span\u003e\u003c/span\u003eis the wood color change due to weathering, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:{L}^{*}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:{a}^{*}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:{b}^{*}\\)\u003c/span\u003e\u003c/span\u003evalues are the color differences and were calculated from measurements made before and after each weathering period.\u003c/p\u003e \u003cp\u003eBy summing up \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:E}_{ab}^{*}\\)\u003c/span\u003e\u003c/span\u003efor all analyzed points in time, the course of the color changes can be taken into account:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\sum\\:_{i-\\text{1,1}}^{n}{\\varDelta\\:E}_{1,n}^{*}=\\:{\\varDelta\\:E}_{\\text{0,1}}+\\:{\\varDelta\\:E}_{\\text{1,2}}+\\dots\\:+\\:{\\varDelta\\:E}_{n-1,\\:n}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eChroma is defined as the Euclidean distance between a color and its achromatic point of the same lightness:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{C}^{*\\:}=\\:\\sqrt{{a}^{*2}+{b}^{*2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn all cases the overall average of 10 samples were used for comparison before and after the specific exposure times.\u003c/p\u003e\n\u003ch3\u003eShannon measure of information (Entropy)\u003c/h3\u003e\n\u003cp\u003eTo assess the transformation of wood surfaces (i.e., change of state) caused by weathering we chose a micro-perspective approach, concerned with the fate of particular components of the system. Photodegradation is a problem with uncertainty since we do not know a priori the outcome of this process. It introduces randomness to the wood structure leading to unpredictability, thus increasing uncertainty (entropy). The central idea of information theory is to offer a quantitative measure of uncertainty. Uncertainty is linked to the potential occurrence of ensemble of states; its magnitude depends on the number of possible states and the probabilities associated with each state. The more likely one of these states, the less able is the system to convey further information. Shannon (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1948\u003c/span\u003e) selected a straightforward logarithmic measure to define the uncertainty associated with the occurrence of the following possible states:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:H=\\sum\\:_{\\text{i}=1}^{\\text{n}}{\\text{p}}_{\\text{i}}\\text{log}\\left(\\frac{1}{{\\text{p}}_{\\text{i}}}\\right)\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere, \u003cem\u003eH\u003c/em\u003e represents the Shannon measure of information and p\u003csub\u003ei\u003c/sub\u003e are the probabilities of each of the \u003cem\u003en\u003c/em\u003e possible states, here normalized values of the factors (where, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{\\text{i}=1}^{\\text{n}}{\\text{p}}_{\\text{i}\\:}=1;\\:\\)\u003c/span\u003e\u003c/span\u003ethe probabilities of all possible events must sum up to unity). It has the maximum value of log(\u003cem\u003eN\u003c/em\u003e) when all possible states (normalized values) are equally probable. Before quantifying information, normalization of both input (environmental inputs) and output (total color change) data occurred, scaling them within the specified range [0 to 1]. This normalization was conducted using Eq.\u0026nbsp;5:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\frac{({\\text{x}}_{\\text{i}}-{\\text{x}}_{\\text{m}\\text{i}\\text{n})}}{{(\\text{x}}_{\\text{m}\\text{a}\\text{x}}-\\:{\\text{x}}_{\\text{m}\\text{i}\\text{n})}}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{x}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{x}}_{\\text{m}\\text{i}\\text{n}}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{x}}_{\\text{m}\\text{a}\\text{x}}\\)\u003c/span\u003e\u003c/span\u003e represent the original, minimum and maximum values of both the input and output variables being normalized.\u003c/p\u003e \u003cp\u003eThe joint entropy \u003cem\u003eH\u003c/em\u003e(\u003cem\u003eI\u003c/em\u003e,\u003cem\u003eO\u003c/em\u003e) is defined as:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:H\\left(I,O\\right)=\\:-\\sum\\:_{\\text{i}=1}^{\\text{i}}\\sum\\:_{\\text{J}=1}^{\\text{o}}\\text{p}\\left({\\text{I}}_{\\text{i}},{\\text{O}}_{\\text{j}}\\right)\\text{l}\\text{o}\\text{g}\\text{p}({\\text{I}}_{\\text{i}},{\\text{O}}_{\\text{j}})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{p}\\left({\\text{I}}_{\\text{i}},{\\text{O}}_{\\text{j}}\\right)\\)\u003c/span\u003e\u003c/span\u003e denotes the joint probability that input (\u003cem\u003eI\u003c/em\u003e) is in state \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{I}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e and output (\u003cem\u003eO\u003c/em\u003e) is in state \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{O}_{\\text{j}}\\)\u003c/span\u003e\u003c/span\u003e. The number of possible states, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\:\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:o\\)\u003c/span\u003e\u003c/span\u003e, may not be the same.\u003c/p\u003e \u003cp\u003eThe central information-theoretical quantity describing the reduction of uncertainty, the information content (transinformation), can be obtained via two routes: first, considering the input entropy \u003cem\u003eH\u003c/em\u003e(\u003cem\u003eI\u003c/em\u003e) (dependent solely on the environmental variable or weathering factors) and the output entropy \u003cem\u003eH\u003c/em\u003e(\u003cem\u003eO\u003c/em\u003e) (dependent solely on the discoloration). If there exists some level of dependence between input weathering factors and output state, both entropies overlap to a certain degree, and their joint entropy \u003cem\u003eH\u003c/em\u003e(\u003cem\u003eI\u003c/em\u003e,\u003cem\u003eO\u003c/em\u003e) will be lesser than the sum of both entropies.\u003c/p\u003e \u003cp\u003eThe amount of overlap is the transinformation \u003cem\u003eT\u003c/em\u003e: \u003cem\u003eT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eH\u003c/em\u003e(\u003cem\u003eI\u003c/em\u003e)\u0026thinsp;+\u0026thinsp;\u003cem\u003eH\u003c/em\u003e(\u003cem\u003eO\u003c/em\u003e) \u0026ndash; \u003cem\u003eH\u003c/em\u003e(\u003cem\u003eI\u003c/em\u003e,\u003cem\u003eO\u003c/em\u003e).\u003c/p\u003e \u003cp\u003eThe difference \u003cem\u003eH\u003c/em\u003e(\u003cem\u003eI\u003c/em\u003e) \u0026ndash; \u003cem\u003eT\u003c/em\u003e(\u003cem\u003eI\u003c/em\u003e;\u003cem\u003eO\u003c/em\u003e) is termed equivocation entropy \u003cem\u003eH\u003c/em\u003e(\u003cem\u003eI\u003c/em\u003e|\u003cem\u003eO\u003c/em\u003e), signifying the uncertainty about the input after knowing the output. Similarly, the difference \u003cem\u003eH\u003c/em\u003e(\u003cem\u003eO\u003c/em\u003e) \u0026ndash; \u003cem\u003eT\u003c/em\u003e(\u003cem\u003eI\u003c/em\u003e;\u003cem\u003eO\u003c/em\u003e) is labeled ambiguity entropy \u003cem\u003eH\u003c/em\u003e(\u003cem\u003eO\u003c/em\u003e|\u003cem\u003eI\u003c/em\u003e), representing the uncertainty about the discoloration when an input is provided. Logarithms were taken to the base 10. For a detailed derivation we refer to Jones and Jones (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2000\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAnalyses were performed using Microsoft Excel software (version 16.87).\u003c/p\u003e"},{"header":"Results (Photodegradation)","content":"\u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eWood color changes after 18 weeks of weathering\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eL*\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ea*\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eb*\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReference state\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e43.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e27.56\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAfter 18 weeks of weathering\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e66.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn relation to the reference state, \u003cem\u003eP. africanum\u003c/em\u003e wood has a low lightness level, as defined by Nishino et al (1998). However, it also exhibits a tendency to move towards the \u003cem\u003eb*\u003c/em\u003e axis, which is indicative of lighter wood. With natural weathering, the \u003cem\u003eL*\u003c/em\u003e value, measuring lightness, exhibited a rise temporally, with a 53% increase rate. The initial darkening phase ended after the first 1.5 weeks, followed by a gradual graying of the samples. The chromatic values (\u003cem\u003ea*\u003c/em\u003e and \u003cem\u003eb*\u003c/em\u003e) decreased over time, approaching zero, indicating that the samples were becoming increasingly achromatic (gray). A graph of the chroma (\u003cem\u003eC*\u003c/em\u003e) and \u003cem\u003eL*\u003c/em\u003e values revealed a more pronounced change after the 10th week, with an increase in lightness and a decrease in chroma (data not shown). After the first week, the total color change (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:E}_{ab}^{*})\\)\u003c/span\u003e\u003c/span\u003e was measured at 3.35, which was noticeable at that time. However, the transformation was not yet complete, and by the 18th week, the total color change had increased significantly to 34.89, resulting in a completely new color. The observed changes in wood color, specifically the increase in lightness and decrease in chromatic values, support the assumption that wood color serves as an indicator of disorganization.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eChange in entropy before and after weathering of color parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eL*\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ea*\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eb*\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReference state\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.7365\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.8194\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7967\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAfter 18 weeks of weathering\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.7592\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7967\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7967\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe degradation of molecules controlling lightness (\u003cem\u003eL*\u003c/em\u003e) is fast (increasing entropy at the end of exposure period (18 weeks)), whereas the degradation of molecules controlling \u003cem\u003ea\u003c/em\u003e* and \u003cem\u003eb\u003c/em\u003e* coordinates are rather slow in \u003cem\u003eP. africanum\u003c/em\u003e. This is analogous to the tendency for stored information about lightness to diminish (initial darkening, then graying). Information initially certain about \u003cem\u003eL*\u003c/em\u003e tends to become uncertain introducing randomness in the lightness of the wood surface thereby resulting in greater effective variability of the exposed wood surfaces. Further chemical analysis is needed to uncover the details of the chemical changes. What we do not know for now is when the entropy reaches its maximum (i.e., completely disorganized or no further disorganization can occur) as biological phenomena have directionality with time (Aoki \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1995\u003c/span\u003e). However, quantitatively the amount of disordering necessary for the loss of darker tone of \u003cem\u003eP. africanum\u003c/em\u003e is 0.0227 after 18 weeks of natural weathering.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eJoint entropies\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWeathering factor\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOutput factor\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eJoint entropy\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSolar irradiance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.1831\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAve. Rainfall\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.1710\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMin. Temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.1212\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMax. Temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.1840\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAve. Temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.1672\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRelative Humidity, 9 am\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.1434\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRelative Humidity, 3 pm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.1497\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSunshine duration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.1774\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal Rainfall\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.1066\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eJoint entropy is a measure of the uncertainty associated with a set of variables (a two-part system). In other words, it represents the total amount of information one has when both input information and output information are known. As the total information in a system, it is the sum of the mutual information, ambiguity, and equivocation. The higher the joint entropy, the greater the degree of disorder or randomness between the two variables. Maximum temperature had the highest joint entropy with total color change whereas total rainfall had the least joint entropy with total color change. From the joint entropy, we can anticipate that maximum temperature may have significant impact on the photodegradation process in \u003cem\u003eP. africanum\u003c/em\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMarginal entropies of the input and output factors\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWeathering factors\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEntropy\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage Rainfall\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.7491\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMax. Temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.8829\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRelative Humidity, 9 am\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.8017\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSunshine Duration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.8829\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSolar Irradiance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.8813\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAve. Temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.8495\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRelative Humidity, 3 pm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.8144\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMin. Temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.7573\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal Rainfall\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.7283\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal Color Change\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.8829\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e gives the summary of marginal entropies of total color change and the weathering factors. These weathering factors are assumed to be information destroyers introducing randomness in the wood surface. They cause stored information to diminish. Marginal entropies are indices of complexity of the factors that are perceived as being most critical for the photodegradation process. It measures nondeterministic or unpredictable behavior of the variables studied. Total rainfall had the minimum entropy, implying a marginally reduced level of uncertainty (\u003cem\u003elow complexity\u003c/em\u003e). There is an elevated level of certainty or confidence in predicting the outcome of total rainfall record or it is more likely to be a particular state. In contrast, total color change, average rainfall, maximum temperature, relative humidity at 9 am, and sunshine duration exhibited the highest entropies (\u003cem\u003ehigh complexity\u003c/em\u003e). From micro-perspective, these variables can be found in different states (or different arrangements of individual states) and thus the more able are they to convey further information. High information of a single factor means that the amount of novelty in that factor (message) is large and, therefore, that uncertainty predominates. The values describe the complexity of the random variable and the amount of hidden or missing information required on average to describe them. For example, one would need an average information of size 0.8829 to describe total color change fully. The average entropy of all the considered weathering factors was 0.8403. Interestingly, the amount of information contained in the output was equal to the information contained in the inputs with highest marginal entropy (0.8829). Expectedly, the contribution of the input information to the output information was not more than the amount of input information.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eMutual information between environmental variables and total color change\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWeathering factors\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOutput Factor\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMutual Information\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMax. Temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5818\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSolar Irradiance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5811\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSunshine Duration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5753\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage Temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5652\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRelative Humidity, 3pm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5476\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRelative Humidity, 9am\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5412\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMin. Temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5190\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage Rainfall\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5149\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal Rainfall\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5046\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eMutual information, also known as transinformation, is interpreted as the average information received by the output transmitted by the input. It gives a measure to the transmitted information between the input and output in a system. In simple terms, it is the decrease in uncertainty (or the gain in certainty) about the output (i.e., discoloration) that is derived from observing a weathering factor. It is the input flow which affects output, representing the strength of the relationship or association between the two random variables. From cybernetics and systems viewpoint, this term is a measure of the degree to which the color of wood samples takes actions coordinated with their immediate surrounding. It is usually referred to as transmission in information theory, measuring the internal constraints in a communication system. It quantifies the degree to which knowledge about the values of one variable diminishes our uncertainty in predicting the values of the other variable. Maximum temperature is informationally rich variable in explaining total color change. Total rainfall gives the least information with total color change. The weathering factors studied communicate some information about wood color; the average amount communicated is 0.5479. The non-zero mutual information implies that wood is not independent of its environment and provides a limit to cope. The wood apparently would be receiving the environmental messages with only about an average of 67% efficiency.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eConditional entropies (equivocation and ambiguity)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWeathering factors\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOutput\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEquivocation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAmbiguity\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSolar Irradiance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3018\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage Rainfall\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2342\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3680\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMin. Temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2383\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3634\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMax. Temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3011\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage Temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2843\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3177\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRelative Humidity, 9 am\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2605\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3417\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRelative Humidity, 3 pm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2668\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3353\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSunshine Duration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2945\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3076\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal Rainfall\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e\u0026#120549;E*\u003c/b\u003e\u003csub\u003e\u003cb\u003eab\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2237\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3783\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e gives a summary of the conditional entropies between the input and output factors. Equivocation measures the uncertainty in the input given the output variable while ambiguity gives the uncertainty in the output given the input variable. From the standpoint of data analysis, equivocation can be considered as a measure of irrelevance of the weathering factors with respect to total color change. Ambiguity averaged 0.3350 with equivocation averaging 0.2671 for all weathering factors. The wood material dedicates relatively higher amount of information to proper functioning of the weathering activity than blocking or discarding the sent environmental information. This can be explained by the fact that wood was not treated to withstand weathering. Alternatively, it is the amount of information generated within the wood block itself and at least not related to the known input is relatively higher than the amount of input information the wood blocks. In other words, higher components of the output (discoloration) are autonomously produced and are unrelated to weathering inputs. One would need a little more information to clarify any input variable if given the color change knowledge than the other way round. Total rainfall recorded the greatest equivocation with minimum temperature the largest ambiguity. Equivocation from cybernetics viewpoint (Conant \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1976\u003c/span\u003e) can be viewed as input flow that is blocked or rejected by the wood whereas ambiguity is the flow internal to the system dedicated to coordinating the degradation process akin to computation (i.e., \u003cem\u003ecomputation\u003c/em\u003e - \u003cem\u003eselection of particular chemical bonds to break upon receiving ultimate information from the sun\u003c/em\u003e). Ambiguity can therefore be referred to as the photodegradation process uncertainty. The blockage of information is an important function of information-processing (smart) materials. They filter the information received from their environment, allowing only the \u0026ldquo;relevant\u0026rdquo; aspects to affect their output.\u003c/p\u003e \u003cp\u003eAmbiguity is the amount of uncertainty per step about color change, given complete knowledge of weathering input. It corresponds to internally-generated information i.e., autonomous behavior, since it corresponds to behavior which has no apparent cause (at least not in the known environmental influences). It can be viewed as noise analogous to that on a communication channel \u0026ndash; a message at the output not caused by a message at the input. It interferes with good communication. With ambiguity and equivocation being non-zero means that even if one has complete knowledge of the weathering factors, there is still residual uncertainty about the weathering output, i.e., \u003cem\u003estate of discoloration\u003c/em\u003e. Also, the \u0026ldquo;channel\u0026rdquo; which links the wood to its environment is a noisy one. These values can be used to measure the performance of a particular wood species resistance to photodegradation. For example, wood with high resistance to weather and UV radiation would have a higher equivocation and lower ambiguity. In other words, the wood would be able to reduce internal coordination to the minimum as soon as possible and block or reject most of UV and visible light radiation (controlled equivocation). Another pathway would be to perform as little blockage as possible by avoiding irrelevant components of the environmental factors.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eDarkening and Graying\u003c/h2\u003e \u003cp\u003eWeathering generally induces a rapid darkening of wood surfaces because of the degradation of lignin and extractives into quinones (darker in color), which are progressively washed out leaving the cellulose-rich wood surface lighter in color as the process progresses.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eInterpretation of the model\u003c/h3\u003e\n\u003cp\u003eThe model presented in this paper may be interpreted in several ways. First, as a method of description, and one particularly suited to complex, active communication. Second, the model makes predictions about photodegradation of wood surfaces, the accuracy of which will depend upon the adequacy of our sample, and the consistency of the discoloration process. In addition, the probability model could be used to simulate photodegradation process, generating records of discoloration sequences that would be difficult to distinguish from real records. Indeed, this similarity is an indication of the adequacy of the model.\u003c/p\u003e\n\u003ch3\u003eMarginal Entropies\u003c/h3\u003e\n\u003cp\u003eThe information measured in Shannon\u0026rsquo;s theory is limited to the syntactic level, focusing on the statistical and structural properties of the signal. What the study has done here is to model a weathering system int terms of input-output relationship using communication system and cybernetics frameworks. The approach has not only revealed the information dynamics and architecture but also quantified the amount of information stored between the input and output and components transmitted within the system. Entropy as a coarse grain property allows us to measure the uncertainty about what happens microscopically or scales many orders of magnitude smaller than the observation scale (Crevecoeur \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Thus, the discoloration was more random resulting from the breaking down of highly organized molecules or simply rearrangement of the molecules inside the wood (Jordan \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eTransmission or transinformation\u003c/h2\u003e \u003cp\u003eTransinformation is the key metric for evaluating and comparing the significance of different weathering factors on discoloration of wood surfaces. It is the amount of information transmitted between the two variables. Mutual information, a measure of relatedness between the input and output variables, accounts for the usefulness in systems science. It reveals hidden relationships and dependencies that do not manifest themselves in the covariance or linear correlation coefficient (Kraskov et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2004\u003c/span\u003e), a kind of generalized correlation. It is a measure of control power as per Bialek (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). It is observed with different names; e.g., \u0026ldquo;\u003cem\u003epredictive information\u003c/em\u003e\u0026rdquo;, \u0026ldquo;\u003cem\u003estored information\u003c/em\u003e\u0026rdquo;, \u0026ldquo;\u003cem\u003eeffective measure complexity\u003c/em\u003e\u0026rdquo; (Shalizi and Crutchfield (2001); Bialek et al. (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2001\u003c/span\u003e); Bialek and Tishby (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1999\u003c/span\u003e); Arnold (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1996\u003c/span\u003e). As a measure of complexity, it characterizes order-to-disorder phase transition in the transformation process. This measure will be referred to as \u003cb\u003ephotodegradation/deteriorative complexity\u003c/b\u003e giving the amount of sensitivity of the wood to weathering factors. It represents the amount of information needed to fully characterize the initial (starting material) and final states of the wood color (Ruth and Bullard, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1993\u003c/span\u003e). A completely reversible process indicates perfect information transmission, whereas any deviation from this ideal situation emphasizes the irreversible nature of the photodegradation process. This is because the color after 18 weeks of weathering resulted in a completely new color as formation of new chemical compounds or structures are different from the original state. A high mutual information indicates a strong correlation between random variables. Specifically, it was observed that the maximum temperature \u0026ldquo;communicated\u0026rdquo; largest information about discoloration, while the total rainfall had the least effect. Changes in the maximum temperature are more likely to result in noticeable changes in the discoloration, while changes in the total rainfall are less predictive of the discoloration. The higher value for information transmission for maximum temperature may be the result of adaptation to photochemical reactions during harsh interactions. Elevated temperature generates higher vibration energy; thus, photons can split chemical bonds more easily than at ambient temperatures (Preklet et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). In the weathering process, elevated temperature can lead to increased photodegradation, as the higher vibration energy makes it easier for photons to break chemical bonds in the wood material. Alternatively, it could imply that the wood has a greater solar irradiation sensitivity at elevated temperatures or possibly energy transfer is reduced at low temperatures. It has been suggested that heat and irradiation may in some way complement each other and that heat exposure alone can cause reactions comparable to UV exposure (Yatagai and Zeronian \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1994\u003c/span\u003e). Solar irradiation was the second most informationally rich variable explaining discoloration. It was only lesser by \u003cem\u003e0.0007\u003c/em\u003e compared to maximum temperature. According to Platzman and Franck (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1956\u003c/span\u003e), the absorption of ultraviolet light does not itself break bonds. The initial acts energy transfer are all ones in which energy is communicated to the electronic systems of molecules; subsequent rearrangement of atomic positions may then result in dissociation. It replaces the notion that solar irradiation acts merely by breaking chemical bonds directly. Solar irradiation and heat provide more or less random methods of disordering the wood biochemical structure.\u003c/p\u003e \u003cp\u003eFinally, the apparent activation energies for the \u003cem\u003eL*\u003c/em\u003e was positive while negative for \u003cem\u003ea*\u003c/em\u003e and \u003cem\u003eb*\u003c/em\u003e, indicating that the reaction decreases slowly with increasing temperature (data not shown). The molecules controlling the brightness are most sensitive to thermal agitations.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eConditional entropies\u003c/h2\u003e \u003cp\u003eThe concepts of equivocation and ambiguity, as outlined in the cybernetics framework (Conant \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1974\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1976\u003c/span\u003e), provide valuable insights into the weathering performance of wood materials. In this study, we have demonstrated how these principles can be applied to understand and predict the degradation of wood exposed to various weathering factors (entropy injectors). Equivocation, defined as the ability of the wood to block or reject certain environmental inputs, was found to be a critical factor in determining the resistance of wood to weathering. It defines the control and regulatory mechanisms of the wood to photodegradation process. Our results show that the wood is able to block or reject a greater amount of information from maximum temperature with solar irradiation as second. The wood, however, either blocks or filters out least amount of information flow from total rainfall. The higher the value of the equivocation, the more input messages must be transmitted and recognized by the wood. Solar irradiation presents more information than needed for chemical cleaving. The wood then blocks as much as possible because the wood is mainly responsive to UV component and some visible light of sunlight. The ability of the wood samples to reject or block some of environmental information packet implies that they exhibit adaptive behavior. Ambiguity, on the other hand, represents the wood\u0026rsquo;s internal computational or processing capabilities that govern its response to weathering factors. Moisture carries stepwise instruction that specifies photodegradation process that transforms the wood colour.\u003c/p\u003e \u003cp\u003eAccording to Eder et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), ambiguity is the intrinsic \u0026ldquo;code\u0026rdquo; or algorithm that determines how the material responds to external stimuli, processes information, and adapts to changing conditions. Moreover, it codes the operation, acting as a sensor for transforming a particular environmental input into output actions. The wood possesses the ability to internally regulate its moisture content in response to fluctuations in relative humidity and temperature. For instance, in our study, the initial moisture content of the wood specimens, starting at 12%, rose to approximately 16% by the end of the exposure period. The internal flow can be linked to a computational activity, where the wood selects which particular chemical bonds to cleave upon receiving \u0026ldquo;ultimate\u0026rdquo; information from the sun\u0026rsquo;s radiation or heat. For complex tasks, the wood would require a lot of internal coordination or calculation that is reflected by the ambiguity. It was found that the specimens required a lot of information coordinating the input flow from total rainfall (i.e., moisture), implying the complexity of the interaction, and thus reducing the mutual information. In contrast, maximum temperature required a smaller amount of information to internally coordinate the information flow and hence high throughput (mutual information). The interaction of wood structure and maximum temperature can therefore be seen as a simple task. Wood is not passively undergoing photodegradation, but is actively \u0026ldquo;computing\u0026rdquo; or processing environmental inputs and orchestrating a specific response in the form of selective bond cleavage and other chemical changes, resulting in the discoloration at the macro state. It is widely believed that intrinsic activity in wood is triggered by the dynamic activity of water as highlighted by Eder et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The transformations induced by water inside the wood serve as the fundamental link between matter and energy. Water replaces functions of electricity in natural materials like wood, acting as a vital interface in the photodegradation process and the hydroxyl groups from lignin, hemicelluloses and cellulose play a key role in this process. This explains how water can wash away fragmented lignin and hemicellulose, as noted by Evans et al. (2015). Furthermore, water enhances light penetration into previously inaccessible areas, effectively opening up new pathways for light to react and interact with the wood, a phenomenon discussed by Feist and Hon (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e1984\u003c/span\u003e). The wood dedicating a larger amount of information to the activity of water implies the cell wall is more hydrophilic rendering the wood more prone to water sorption. Water then completely breaks hydrogen bonds in the amorphous part of the wood. As the photodegradation process progresses, the wood undergoes cycles of water uptake and loss resulting in visible swelling and shrinking.\u003c/p\u003e \u003cp\u003eFrom a cybernetics viewpoint, wood as an active biological material can thus be considered as a machine \u0026ndash; molecular one (Bensaude-Vincent \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Eder et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The question that arises is whether there are optimal values for transinformation, equivocation, and ambiguity. An optimized system, as defined by Jantsch (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e1980\u003c/span\u003e), should maintain a balance of approximately 50% equivocation and ambiguity and 50% confirmation (transinformation). This balance suggests that the system is functioning efficiently and effectively, with a sufficient level of uncertainty and novelty to support learning and adaptation, while also providing enough structure and predictability to enable successful communication and coordination. These findings have important implications for design and development of more sustainable wood-based materials. There are some limitations in the methods used in this study that should be noted. There are several weathering factors which have not been considered here. First, no information has been made for chemistry of wood and air quality for example. Secondly, it was not possible to interpret discoloration which could possibly have a function in \u0026ldquo;metacommunication\u0026rdquo;, i.e., communication that affects the interpretation of other communication. Even with these limitations, however, the statistical method undertaken is a powerful tool for analyzing communications systems and weathering systems. It demonstrates, first, that communication is occurring between the wood and its environmental variables. Actual changes in wood colour do occur following the execution of specific acts by environmental variables.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study demonstrates how the concepts of random variables and probability distributions can be applied to uncover the mathematical framework underlying complex physical processes, such as photodegradation. By modelling the inherent effective variability and uncertainty in environmental factors and material responses, we provide a quantitative foundation for predicting degradation outcomes and understanding the mechanisms driving these changes. Our findings indicate that specific environmental factors \u0026ndash; such as moisture, solar irradiation and maximum temperature \u0026ndash; play crucial roles in influencing wood discoloration. Notably, we identified the signals that convey the most information regarding these changes, providing insights into the dynamics of wood discoloration.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDisclosure statement\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo potential conflict of interest was reported by the authors.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAoki I (1995) Entropy production in living systems: from organisms to ecosystems. Thermochimica Acta 250:359–370.\u003c/li\u003e\n \u003cli\u003eArnold DV (1996) Information-theoretic analysis of phase transitions. Complex Systems 10:143–155.\u003c/li\u003e\n \u003cli\u003eBensaude-Vincent B (2011) Materials as machines. 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Cellulose 1:205–214. \u003cbr\u003e \u003cbr\u003e \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Complexity, Entropy, Information Theory, Material transformation, Mutual information, Order, Randomness, Photodegradation","lastPublishedDoi":"10.21203/rs.3.rs-6305182/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6305182/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWood is a structured biomaterial able to interact with its environment. An information theoretic framework has been used to model the processing of the environmental inputs to produce output (discoloration) in a photodegradation process. The task of the wood is to receive signals from source with its molecular structure, lignin, acting as the sensor, process them to produce output, blocking \u0026ldquo;irrelevant\u0026rdquo; information, coordinating the activities of the internal processing. Maximum temperature (heat) was found to be the most informationally rich environmental input affecting discoloration whereas the wood dedicated a large amount of information to the activities of total rainfall (moisture). The wood blocked greatest amount of information of the sent information by maximum temperature. If the intensity of photodegradation is to be reduced, the wood must be protected from maximum temperature (heat) and moisture. When viewed from this perspective, the active and intelligence nature of wood is reinforced.\u003c/p\u003e","manuscriptTitle":"Application of Information Theory to Study Wood Photodegradation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-22 14:51:54","doi":"10.21203/rs.3.rs-6305182/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"166fbc95-43d7-4a82-b931-96d5914a0a2a","owner":[],"postedDate":"April 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-05-05T16:38:33+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-22 14:51:54","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6305182","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6305182","identity":"rs-6305182","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}