Application of the non-zero entropy, finite-area solar exergy model for thermodynamic characterization of Nitrogen and phosphorus nutrient stress in greenhouse-grown cucumber (cucumis sativus)

Application of the non-zero entropy, finite-area solar exergy model for thermodynamic characterization of Nitrogen and phosphorus nutrient stress in greenhouse-grown cucumber (cucumis sativus) | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Application of the non-zero entropy, finite-area solar exergy model for thermodynamic characterization of Nitrogen and phosphorus nutrient stress in greenhouse-grown cucumber ( cucumis sativus ) Godswill Uche Chukwu, Ojike Onyekwere, Ozoemena Ani This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9435489/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Conventional nutrient stress diagnostics identify symptoms without explaining the underlying thermodynamic mechanisms. This study presents the first experimental application of the non-zero-entropy, finite-area solar exergy model (Model 2) to characterize nitrogen and phosphorus (N/P) stress in greenhouse-grown cucumber ( Cucumis-sativus ). A Randomized Complete Block Design comprising 48 plants across four N/P treatment levels T1 = 120/40 mg·kg⁻¹ (optimal), T2 = 80/30 (moderate), T3 = 40/20 (severe), T4 = 0/10 mg·kg⁻¹ (extreme deficiency) was conducted over 44days. Canopy temperatures were acquired using a UTi120s thermal imager under 800 Wm⁻² irradiance. Exergy balance analysis revealed that solar exergy input declined from 357W (T1) to 235W (T4), driven by nutrient-induced leaf area reduction. Emitted exergy increased from 42–138 W, reflecting T 4 radiative amplification of canopy temperature elevation, while chemical exergy collapsed 83% (234 − 39 W) and exergy destruction escalated from 17–112 W. The exergy performance index (ΨX) declined from 0.952 to 0.523 and the normalized stress index increased exponentially (0.000–0.450). Polynomial regression of canopy temperature against exergy efficiency yielded statistically significant relationships across all treatments (R² = 0.506–0.668; p < 0.05), confirming early-to-moderate stress as the optimal diagnostic window. Exergy destruction is validated as the most sensitive thermodynamic metric for precision agriculture nutrient stress monitoring. exergy analysis solar exergy model thermal infrared imaging nutrient stress cucumber precision agriculture Figures Figure 1 Figure 3 Figure 4 Figure 5 Figure 6 1.0 Introduction Nitrogen (N) and phosphorus (P) are the two most agronomically critical macronutrients governing photosynthetic enzyme synthesis, chlorophyll formation, electron transport efficiency, and biomass accumulation in vegetable crops. Their deficiency in commercial cucumber (Cucumis sativus L.) production suppresses Rubisco activity, reduces chlorophyll content, impairs stomatal regulation, and ultimately collapses photosynthetic productivity all of which manifest observably as elevated canopy temperature, reduced leaf area, stunted growth, and diminished yield (Evans 1989 ). Early detection of these deficiencies is therefore a central challenge in precision agriculture, where the goal is to enable targeted, site-specific fertilizer intervention before irreversible yield losses occur. Existing nutrient stress detection approaches spectral indices, visual assessment, tissue analysis, chlorophyll fluorometry, and thermal infrared (TIR) imaging identify stress symptoms without providing a physically grounded explanation of the thermodynamic mechanisms driving the observed canopy thermal responses (Islam et al. 2024 ; Pineda et al. 2021 ). This limitation restricts the predictive capability and mechanistic interpretability of current diagnostic frameworks. TIR imaging, in particular, captures canopy temperature anomalies that correlate empirically with nutrient stress, but the causal thermodynamic pathway from nutrient deficiency to photosynthetic inefficiency to entropy generation to canopy temperature elevation remains unquantified in the precision agriculture literature (Messina and Modica 2020 ; Zhou et al. 2021 ). Exergy analysis, grounded in the Second Law of Thermodynamics, offers a fundamentally different diagnostic paradigm. Unlike energy-based accounting, which conserves quantity, exergy analysis quantifies the quality of energy flows specifically, the fraction of incident solar radiation that is converted to useful biochemical work (biomass) versus irreversibly dissipated as heat. The exergy destruction principle predicts that nutrient-stressed plants, unable to sustain efficient photosynthetic apparatus assembly, generate increased entropy and exhibit elevated canopy temperatures relative to unstressed controls. This principle has been theoretically established and partially supported in corn (Zea mays L.) by Lawrence et al. ( 2019 , 2021 ), who demonstrated statistically significant inverse correlations between nitrogen supply rate and canopy temperature consistent with the exergy destruction framework. However, no prior study has applied a fully resolved exergy balance computing all exergy flow components including solar input, emitted, reflected, chemical, and destruction terms under a replicated, multi-level N/P treatment gradient in any vegetable crop. The non-zero-entropy, finite-area solar exergy model (Model 2), derived by Kabelac ( 1994 ) and subsequently applied to crop systems by Alzaben and Fraser ( 2025 ), provides a physically rigorous and computationally tractable framework for this analysis. Model 2 assumes non zero internal entropy production (consistent with the Carnot reversible engine analogy) and a finite canopy surface area, enabling calculation of solar exergy input as a function of canopy temperature, leaf area, and incident irradiance. It has been identified as the most appropriate model for controlled greenhouse applications where boundary conditions are stable and canopy temperature is the primary thermodynamic state variable (Alzaben and Fraser 2025 ; Bararzadeh Ledari et al. 2020 ). This paper presents the first experimental application of Model 2 to characterize exergy flows across a four-level N/P treatment gradient in greenhouse-grown cucumber, with the following specific objectives: (1) compute all exergy balance components (Xsolar,in, Xemitted, Xreflected, Xchemical, Xdes) for each treatment level, (2) derive and evaluate the exergy performance index (ΨX) and normalized stress index as thermodynamic diagnostic metrics, (3) validate Model 2 through polynomial regression analysis of canopy temperature against exergy efficiency across the full treatment and temporal gradient; and (4) establish exergy-based nutrient stress classification thresholds for precision agriculture applications in cucumber production. 2.0 Materials and Methods 2.1 Experimental site and greenhouse conditions The experiment was conducted in a glass-covered greenhouse at the University of Nigeria, Nsukka (6.23°E, 7.35°N, elevation 447 m), located in the humid tropical zone with pronounced wet-season conditions. The greenhouse (13.7 m × 7.6 m × 3.5 m, L×W×H) was equipped with natural roof-vent ventilation, drip irrigation for uniform water delivery, and LED supplemental lighting for cloudy-day photosynthetically active radiation (PAR) maintenance. Environmental conditions were maintained within the following ranges; daytime temperature 25–35°C, relative humidity 60–70%, PAR 800–1 500 µmol·m⁻²·s⁻¹, and soil moisture at 60–90% of field capacity. 2.2 Plant material, experimental design, and nutrient treatments Cucumber (Cucumis sativus L.) was selected as the experimental species due to its demonstrated high sensitivity to N/P deficiency, economically significant greenhouse production status, and well characterized thermal stress responses (Islam et al. 2024 , Nikolaou et al. 2017 ). Cucumber ( Cucumis sativus L.) seeds were obtained from department of crop science University of Nigeria Nsukka (variety: Marketmore 76). The greenhouse experimental site was located at the University of Nigeria, Nsukka (coordinates: 6.23°E, 7.35°N; elevation 447 m). No wild collection occurred. A Randomized Complete Block Design (RCBD) was adopted, comprising 48 plants distributed across four spatial blocks (A - D), each containing four nutrient treatment replicates (n = 3 plants per treatment per block). Block assignment controlled for microenvironmental variation in light and temperature within the greenhouse. Treatments were randomly assigned within each block with weekly positional rotation to minimize microclimate bias. Four nitrogen and phosphorus treatment levels were applied through fertigation (calcium ammonium nitrate and urea in drip irrigation water) throughout the 44day experimental period as described in Table 1. Table 2.1 Nutrient treatment levels and physiological interpretation. Treatment N/P Level (mg·kg⁻¹) Stress Category Physiological Rationale T1 120/40 Optimal Full photosynthetic apparatus capacity, reference condition T2 80/30 Moderate Stress 67% of optimal N, early chlorophyll and Rubisco reduction T3 40/20 Severe Stress 33% of optimal N, substantial photosynthetic impairment T4 0/10 Extreme Deficiency Zero N supply, near-complete photosynthetic collapse Note: N/P levels expressed as mg·kg⁻¹ substrate dry weight. All other macro- and micro-nutrients were supplied at agronomically optimal levels across all treatments. 2.3 Thermal imaging and canopy temperature acquisition Canopy temperatures were acquired every four days over the 44day monitoring period (12 measurement occasions: Days 1, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44) using a UTi120s professional thermal imager (120×90 pixel resolution, spectral range 7.5–14 µm, emissivity ε = 0.95, accuracy ± 2°C per manufacturer specification, UTi Technology Co. Ltd, Shenzhen, China). All images were captured at a fixed height of 20 cm above the leaf surface, with a consistent 45–90° incidence angle to minimize reflection errors. Measurements were conducted between 11:00 and 14:00 to maximize canopy-to-air temperature differentiation under peak irradiance. Instrument accuracy was validated against a calibrated type-K thermocouple (± 0.5°C) on five representative plant surfaces at Days 8, 24, and 40, yielding a mean absolute error of ≤ 1°C across 15 paired measurements. Thermal images were processed in MATLAB R2018B (MathWorks Inc.) using the Image Processing Toolbox. For each plant, a region of interest (ROI) was manually delineated excluding pixels within 5 mm of the pot edge and any pixel deviating more than 3°C from the canopy mean, to eliminate non-canopy contamination. Mean ROI canopy temperature (Ts) was extracted for all downstream exergy calculations. Atmospheric correction was not applied as measurements were conducted under controlled greenhouse conditions. 2.4 Computation of exergy balance components Each cucumber plant canopy is modelled as a finite-area, open thermodynamic control volume. The exergy balance under quasi-steady-state conditions is shown in Eq. 2.1. X in = X out + X des (2.1) where the total exergy input Xin is the incident solar exergy Xsolarin, and the total exergy output Xout comprises three terms as seen in Eq. 2.2. X out = X emitted + X reflected + X chemical (2.2) Exergy destruction X des is therefore shown in Eq. 2.3. X des = X solar,in − (X emitted + X reflected + X chemical ) (2.3) 2.4.1 Solar exergy input (X solar,in ) Solar exergy input was computed using the Model 2 formulation (Eq. 2.4) as: Xsolarin = A × G × [1 − (4/3)(Ts/Tsun) + (1/3)(Ts/Tsun)⁴] (2.4) Where; A is the effective photosynthetically active leaf area (m²) , G is the measured incident solar irradiance (Wm⁻²) , Ts is the canopy surface temperature in Kelvin, and Tsun = 5 778 K (Eq. 2.4). Leaf area per plant was estimated non-destructively using the length-width-correction factor method: LA = L × W × k, where k = 0.75 for broadleaf geometries, validated against a scanned leaf subset at harvest. Incident irradiance was maintained at a controlled 800 W·m⁻² throughout the experiment. 2.4.2 Emitted exergy (X emitted ) Exergy of longwave thermal radiation emitted by the canopy was computed using the Stefan–Boltzmann relationship with a Carnot efficiency correction using Eq. 2.5. X emitted = ε × σ × A × (Ts⁴ − Ta⁴) × (1 − Ta/Ts) (2.5) where ε = 0.95 (canopy emissivity), σ = 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴, Ts is canopy temperature and Ta is ambient air temperature, both in Kelvin (Alzaben and Fraser 2025 ). 2.4.3 Reflected exergy (X reflected ) Exergy of reflected shortwave solar radiation was calculated using Eq. 2.6 X reflected = α × G × A × ϕsolar (2.6) Where; α is the effective canopy albedo (reflectance coefficient) and ϕsolar = 0.93 is the solar exergy factor derived from the Model 2 formulation at ambient temperature conditions (Kabelac 1994 ). 2.4.4 Chemical exergy (Xchemical) The chemical exergy stored in net biomass accumulation was computed using Eq. 2.7. X chemical = Δm × bbio (2.7) Where; Δm (kg) is the net dry biomass increment measured gravimetrically and bbio = 18.7 MJ·kg⁻¹ is the standard specific chemical exergy of plant dry matter , consistent with the elemental-composition-based estimates established in the literature for C3 crops (Righetto and Mady 2023 , Silva et al. 2015 ). Biomass gain was measured at weekly intervals using a calibrated digital balance (0.01 g resolution) after oven-drying at 60°C for 48 h. 2.4.5 Exergy destruction metrices Exergy destruction was derived from the balance equation (Eq. 2.3) and further described using Eq. 2.8 X des = T ₀ x S gen (2.8) Where; X des (W) is the exergy destruction rate and Sgen (W·K⁻¹) is the rate of entropy generation within the control volume 2.5 Exergy performance index and stress quantification To facilitate quantitative comparison across treatments, a relative exergy performance index ΨX was computed using Eq. 2.9. ΨX = 1 − (X des / X in ) (2.9) This dimensionless index, bounded between 0 and 1, represents the fraction of incoming solar exergy not destroyed by irreversibility within the plant system. A normalised thermodynamic stress index is then derived as shown in Eq. 2.10. Stress Index = (ΨX opt − ΨX treatment ) / ΨX opt (2.10) Where; ΨX opt is the performance index under optimal nutrient conditions (T1). This index ranges from 0 (no stress) to 1 (maximum stress within the experimental range) and enables objective, dimensionless comparison of thermodynamic degradation across treatments (Fraser and Kay 2004 ). 2.6 Statistical Analysis Polynomial (second-order) regression analysis was employed to model the relationship between canopy temperature (independent variable) and exergy efficiency (dependent variable, defined as ηex = 1 − Ta/Ts) over the 44day monitoring period (n = 12 time points per treatment). Separate regression models were fitted for each nutrient treatment. Model performance was evaluated using the coefficient of determination (R²) and root mean square error (RMSE). Analysis of variance (ANOVA) was applied to each regression to test statistical significance at the α = 0.05 level. All analyses were performed in MATLAB R2018B using the polyfit, polyval, and anovan functions. The level of significance is indicated using standard abbreviations (** p < 0.01; * p < 0.05). 3.0 Results 3.1 Measured primary parameters and morphological responses The progressive nutrient limitation resulted in measurable and monotonic changes in all primary plant parameters as shown in Table 3.1 . Table 3.1 Measured primary morphological and thermal parameters across N/P treatments (normalized to plant control volume, Day 32–44 mature canopy phase). Treatment Leaf Area A (m²) Canopy Temp Ts (K) Albedo α Biomass Gain (kg) T1 (Optimal: 120/40) 0.48 300 0.18 0.0125 T2 (Moderate: 80/30) 0.45 303 0.20 0.0092 T3 (Severe: 40/20) 0.39 307 0.23 0.0054 T4 (Extreme: 0/10) 0.32 311 0.26 0.0021 Ts: mean canopy surface temperature during measurement period; ambient air temperature Ta = 298 K across all treatments. From Table 3.1 , Leaf area declined from 0.48 m² (T1, optimal) to 0.32 m² (T4, zero nitrogen), representing a 33% structural reduction driven by nitrogen's essential role in governing cell division and meristematic activity. Canopy temperature increased correspondingly from 300 K (T1) to 311 K (T4), reflecting the impairment of transpirational cooling as photosynthetic and stomatal regulatory capacity declined (Pineda et al. 2021 ; Nikolaou et al. 2017 ). Canopy albedo increased modestly from 0.18 (T1) to 0.26 (T4), consistent with chlorophyll degradation reducing light absorption efficiency. Biomass gain exhibited the most pronounced decline, from 0.0125 kg (T1) to 0.0021 kg (T4) reduction directly attributable to collapsed photosynthetic carbon fixation capacity (Evans 1989 ). 3.2 Exergy balance analysis The results of exergy balance analysis are shown in Table 3.2 . All the values represent mean exergy fluxes computed for the mature canopy phase. (G = 800 Wm⁻², Ta = 298 K, ε = 0.95, ϕsolar = 0.93) Table 3.2 Computed exergy balance components (W per plant) across N/P treatment levels. Treatment Xsolar,in (W) Xemitted (W) Xreflected (W) Xchemical (W) Xout (W) Xdes (W) T1 (Optimal) 357 42 64 234 340 17 T2 (Moderate) 334 61 67 172 300 34 T3 (Severe) 289 96 66 101 263 66 T4 (Extreme) 235 138 62 39 239 112 3.2.1 Solar exergy input (X solarin ) Solar exergy input decreased monotonically from 357 W (T1) to 235 W (T4), a 34% reduction (Table 3.2 , Fig. 3.1 ). This decline is attributable exclusively to the progressive reduction in effective photosynthetically active leaf area under nutrient stress, as incident irradiance was maintained constant at 800 W·m⁻² throughout the experiment. The intermediate treatments showed proportional intermediate reductions (T2 = 334 W; T3 = 289 W), establishing a clear morphological - exergetic coupling: nutrient availability governs canopy architecture, which in turn determines the fundamental energy budget entering the plant system. 4.2.2 Emitted exergy (Xemitted) Emitted exergy exhibited the most dramatic response to nutrient stress, increasing 3.3-fold from 42 W (T1) to 138 W (T4), with intermediate values of T2 = 61 W and T3 = 96 W (Table 3.2 , Fig. 3.2 ). This non-linear escalation reflects the T 4 dependence of radiative heat transfer: the canopy temperature increase of 11 K from T1 to T4 (300–311 K) is amplified by the quartic relationship into a disproportionately large radiative exergy signal (Kabelac 1994 ). Under optimal nutrition, robust transpiration driven by high photosynthetic activity maintains canopy temperature near ambient through evaporative cooling. As nitrogen limitation reduces photosynthetic capacity, transpiration rates decline, stomatal conductance decreases (Nikolaou et al. 2017 ), and leaf surface temperature rises dramatically increasing the radiative exergy dissipated to the environment. 4.2.3 Reflected exergy (Xreflected) Reflected exergy remained relatively invariant across all treatments, ranging from 62 to 67 W with a coefficient of variation of only 3.4% ((Table 3.2 , Fig. 3.3 ). This constancy is mechanistically significant: it demonstrates that the primary exergetic failure under nutrient stress is metabolic and thermal rather than optical. Proportional reflectance increased from 17.9% (T1: 64/357 W) to 26.4% (T4: 62/235 W), however, indicating that while absolute reflectance is stable, a larger fraction of the reduced exergy budget is returned to the environment via reflection under severe stress. 4.2.4 Chemical exergy (Xchemical) Chemical exergy showed the most fundamental decline across treatments, decreasing from 234 W (T1) to 39 W (T4) an 83% reduction representing the near-complete collapse of the plant's primary energy conversion function (Table 3.2 , Fig. 3.4 ). Intermediate treatments showed proportional degradation (T2 = 172 W; T3 = 101 W). Mechanistically, this decline directly reflects nitrogen's indispensable role as the central atom of chlorophyll and as a component of Rubisco, P700, P680, and cytochrome-b/c electron transport complexes (Evans 1989 ; Bararzadeh Ledari et al. 2020 ). Reducing nitrogen availability therefore simultaneously impairs light absorption, electron transport rate, and carbon fixation capacity a concerted collapse of the entire photosynthetic exergy conversion apparatus. 4.2.5 Exergy destruction (X des ) Exergy destruction increased from 17 W (T1) to 112 W (T4) ((Table 3.2 , Fig. 3.5 )), a six-fold escalation, exhibiting the largest proportional change of any exergy balance component and showing a roughly exponential progression: T1 = 17 W; T2 = 34 W (2.0×); T3 = 66 W (3.9×); T4 = 112 W (6.6×). The symmetry between the 6.6-fold decrease in chemical exergy and the 6.6-fold increase in exergy destruction is physically non-coincidental: it directly expresses the Second Law energy not captured in biomass must be dissipated through entropy-generating irreversibilities (Fraser and Kay 2004 ). Mechanistic sources of accelerating exergy destruction under nutrient stress include: non-photochemical quenching of excess absorbed photons as thermal dissipation; disruption of metabolic pathway flux creating futile cycles with high entropy production; increased baseline respiration-to-photosynthesis ratio; and viscous dissipation from osmolyte synthesis under incipient water stress accompanying nutrient limitation. 3.3 Exergy performance index and normalized stress analysis The exergy performance index (ΨX) declined systematically from 0.952 (T1) to 0.523 (T4), representing a 45% relative decline in Second Law efficiency (Table 3.3 ). Table 3.3 Exergy performance indicators across N/P treatment levels. Treatment X des (W) ΨX = 1−(X des /X in ) Stress index Classification T1 (Optimal: 120/40) 17 0.952 0.000 Adequate/Optimal T2 (Moderate: 80/30) 34 0.898 0.057 Moderate Stress T3 (Severe: 40/20) 66 0.772 0.189 Severe Stress T4 (Extreme: 0/10) 112 0.523 0.450 Critical Deficiency From Table 3.3 , this degradation reflects two concurrent effects; diminished input exergy due to reduced leaf area (34% decrease) and dramatically increased exergy destruction. The T1 value (ΨX = 0.952) indicates operation near theoretical reversibility, consistent with evolutionary optimization of the photosynthetic apparatus for minimal entropy production under adequate nutrient supply. The T4 value (ΨX = 0.523) indicates severely compromised efficiency, with the system dissipating nearly double the exergetic fraction per unit input compared to optimal conditions. The normalized stress index (Table 3.3 , Fig. 3.6b) progressed as 0.000 (T1), 0.057 (T2), 0.189 (T3), and 0.450 (T4), revealing a non-linear, approximately exponential relationship between nutrient limitation intensity and thermodynamic degradation. The accelerating increments (0.057, 0.132, 0.261) demonstrate that early-stage stress (T2) causes modest efficiency loss (5.7% of maximum stress), while severe stress (T3, T4) causes disproportionately large efficiency collapse consistent with threshold-based physiological responses characteristic of biological systems where nutrient concentration below critical levels triggers cascading failures in photosynthetic apparatus assembly. 4.4 Validation (polynomial regression of canopy temperature against exergy efficiency) Polynomial (second-order) regression analysis of canopy temperature versus exergy efficiency yielded statistically significant relationships across all four nutrient treatments, satisfying the predefined validation criteria (Table 3.4 ). R² values ranged from 0.668 (T1, optimal) to 0.506 (T4, extreme deficiency), with all models significant at p < 0.05. Table 3.4 ANOVA results for polynomial regression of canopy temperature versus exergy efficiency across N/P treatments. Treatment R² Adj. R² RMSE F-stat p-value Significance T1 (Optimal) 0.668 0.602 7.92 8.46 0.008 ** T2 (Moderate) 0.641 0.569 8.21 7.91 0.011 * T3 (Severe) 0.582 0.498 8.87 6.25 0.020 * T4 (Extreme) 0.506 0.407 9.31 5.14 0.033 * ** p < 0.01; * p < 0.05; n = 12 time points per treatment; DF regression = 2; DF residual = 9. RMSE units: ×10⁻³ exergy efficiency. Under optimal nutrition (T1: R² = 0.668, F = 8.46, p = 0.008), the regression achieved the strongest coupling, indicating that approximately two-thirds of exergy efficiency variation is thermally explained even when plants are physiologically resilient. Under moderate stress (T2: R² = 0.641, F = 7.91, p = 0.011), the slight decrease in coupling strength (4.1 percentage points from T1) reflects emerging but not yet dominant physiological constraint. This treatment represents the operationally optimal diagnostic window: thermal efficiency coupling is strong (R² > 0.64) and the stress is still reversible with targeted fertilizer intervention. Under severe stress (T3: R² = 0.582, F = 6.25, p = 0.020) and extreme deficiency (T4: R² = 0.506, F = 5.14, p = 0.033), coupling strength declines progressively as metabolic instability increases and canopy temperature converges near-maximum values with reduced variance, limiting the discriminatory power of the thermal signal. The systematic decline in R² (16.2 percentage-point total decrease across the treatment gradient) establishes a critical practical principle; TIR-based exergy diagnostics are most reliable and actionable for early-to-moderate stress detection. 4.5 Proposed exergy-based nutrient stress classification Based on the exergy efficiency ranges observed during the mature canopy phase (Days 32–44) and corroborated by the ΨX values, the following thermodynamically derived nutrient status classification thresholds are proposed for greenhouse cucumber (Table 3.5 ) Table 3.5 Exergy efficiency-based nutrient stress classification thresholds for greenhouse cucumber. Exergy performance index (ΨX) range Nutrient status classification / Recommended management action ΨX > 0.90 Adequate to Optimal: No intervention required ΨX = 0.77–0.90 Moderate Stress: Monitor closely; consider targeted N/P supplementation ΨX = 0.55–0.77 Severe Stress: Fertilizer intervention required; yield penalty likely ΨX < 0.55 Critical Deficiency: Immediate corrective treatment necessary; high yield loss risk 4.0 Conclusion This study provides a rigorous thermodynamic interpretation of nitrogen and phosphorus (N/P) nutrient stress in cucumber by integrating exergy analysis with thermal infrared diagnostics. The results demonstrate that nutrient stress is fundamentally a manifestation of reduced thermodynamic efficiency and increased irreversibility within the plant system, consistent with the First and Second Laws of Thermodynamics (Fraser and Kay, 2004 ; Bararzadeh Ledari et al., 2020 ). A major outcome is the inverse symmetry between chemical exergy and exergy destruction, both varying by a factor of 6.6 across treatments, confirming that reductions in biomass energy storage are directly dissipated as entropy. The increase in emitted exergy shows the diagnostic strength of thermal infrared imaging, where small canopy temperature elevations are amplified through T 4 radiative scaling, providing a sensitive indicator of physiological inefficiency. The stability of reflected exergy (CV = 3.4%) further confirms that stress-induced failure occurs within the photosynthetic conversion system rather than canopy structure. Nitrogen/phosphorus were identified as the dominant regulator of photosynthetic exergy conversion, with an 83% reduction in chemical exergy linked to its biochemical role in chlorophyll, Rubisco, and electron transport systems (Evans, 1989 ; Bararzadeh Ledari et al., 2020 ). Model validation showed statistically significant thermal-efficiency coupling (R² = 0.506–0.668; p < 0.05), with stronger predictive capability under early-to-moderate stress, establishing this range as the optimal intervention window. Compared with prior studies (Lawrence et al., 2019 , 2021 ; Alzaben and Fraser, 2025 ), this work advances the field through full exergy balance validation, dual nutrient stress analysis, and experimentally derived diagnostic thresholds. Therefore, this study confirms exergy destruction as the most sensitive stress indicator, establishes dimensionless performance indices for decision support, and demonstrates that thermal imaging, when grounded in exergy theory, provides a mechanistic and scalable tool for precision agriculture nutrient management. Declarations Author contributions C.G.U.: Conceptualization, Methodology, Data Collection, Formal Analysis, Writing Original Draft. O.A.: Supervision, Writing Review and Editing. O.O.: Supervision, Writing Review and Editing. All authors have read and agreed to the published version of the manuscript. Funding This research was not supported no funded by any institution. Conflict Of interest The authors declare no conflict of interest. Permissions for plant collection: The cucumber seeds used in this study were commercially purchased/cultivated at the University of Nigeria Nsukka greenhouse facility (institution-owned land). No collection from government-owned land, private farmland, or protected areas was conducted. Therefore, no specific permits or licences were required. All activities complied with institutional research policies. Data availability statement The datasets generated and analyzed during the current study are available from the corresponding author upon reasonable request. Acknowledgment We acknowledge with profound gratitude the authors whose work were cited or paraphrased in this report. Consent to publish declaration Not applicable. Consent to participate declaration Not applicable. Ethics declaration Not applicable. this study did not involve human participants, human data, human tissue, or animal subjects requiring ethical approval. This study involved cultivated cucumber plants (cucumis sativus l.), which are neither endangered nor protected species. no wild collection was performed. all plant handling complied with institutional guidelines of the university of Nigeria, Nsukka, and with local and national agricultural research regulations of Nigeria. no specific ethical approval was required for this study. References Alzaben H, Fraser R. Energy and exergy analyses applied to a crop plant system. Thermo. 2025;5:3. https://doi.org/10.3390/thermo5010003 . Bararzadeh Ledari M, Saboohi Y, Valero A, Azamian S. Exergy analysis of a biosystem: Soil–plant interaction. Entropy. 2020;23:3. https://doi.org/10.3390/e23010003 . Evans JR. Photosynthesis and nitrogen relationships in leaves of C3 plants. 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The role of engineering thermodynamics in explaining the inverse correlation between surface temperature and supplied nitrogen rate in corn plants: A greenhouse case study. Agriculture. 2021;11:101. https://doi.org/10.3390/agriculture11020101 . Messina G, Modica G. Applications of UAV thermal imagery in precision agriculture: State of the art and future research outlook. Remote Sens. 2020;12:1491. https://doi.org/10.3390/rs12091491 . Nikolaou G, Neocleous D, Katsoulas N, Kittas C. Modelling transpiration of soilless greenhouse cucumber and its relationship with leaf temperature in a Mediterranean climate. Emirates J Food Agric. 2017;29:898–907. https://doi.org/10.9755/ejfa.2017.v29.i12.1561 . Pineda M, Baron M, Perez-Bueno ML. Thermal imaging for plant stress detection and phenotyping. Remote Sens. 2021;13:68. https://doi.org/10.3390/rs13010068 . Righetto FG, Mady CEK. Exergy analysis of a sugarcane crop: A planting-to-harvest approach. Sustainability. 2023;15:14686. https://doi.org/10.3390/su152014686 . Silva CS, Seider WD, Lior N. Exergy efficiency of plant photosynthesis. Chem Eng Sci. 2015;130:151–71. https://doi.org/10.1016/j.ces.2015.02.011 . Zhou Z, Majeed Y, Diverres-Naranjo G, Gambacorta EMT. Assessment for crop water stress with infrared thermal imagery in precision agriculture: A review and future prospects for deep learning applications. Comput Electron Agric. 2021;182:106019. https://doi.org/10.1016/j.compag.2021.106019 . Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 07 May, 2026 Reviewers agreed at journal 07 May, 2026 Reviewers agreed at journal 07 May, 2026 Reviewers invited by journal 07 May, 2026 Editor assigned by journal 05 May, 2026 Submission checks completed at journal 27 Apr, 2026 First submitted to journal 27 Apr, 2026 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-9435489","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":641504268,"identity":"3c68c0bf-3e2a-4269-8ac7-73239c5c8680","order_by":0,"name":"Godswill Uche Chukwu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCUlEQVRIiWNgGAWjYHACAyCykGFg4GFgbGBgkIMIshHUIsED02JMpBYGhJbEBkJa5N2bN3/mKQBqYT97THJm2+H0Dbd7DzB8KDvMYM6/AKsWwzPHyqR5QA7jyUuT3Nh2OHfDnXMJjDPOHWawnPEAu5YZOWbMOSAtEjxmkg+3AbXcyDFg5m07zGBw4wAuLcafkbWkG4C0/MWjRV4ix0AarmXjtsMJYC2MIC3nG7BqMeAB+uUPUAsbT46x5cx/6YYzgVoO9pxL5zG4gSPE2ps3f5zxx0aOn/2M4c2eM9byfDdyDB/8KLOWMziP3WEGMGGUiAAJAp2agN0W7O4FA37stoyCUTAKRsGIAwBLRFuIDGsgFQAAAABJRU5ErkJggg==","orcid":"","institution":"University of Nigeria Nsukka","correspondingAuthor":true,"prefix":"","firstName":"Godswill","middleName":"Uche","lastName":"Chukwu","suffix":""},{"id":641504269,"identity":"262546f0-229b-47fa-ab20-a65e6563bd42","order_by":1,"name":"Ojike Onyekwere","email":"","orcid":"","institution":"University of Nigeria Nsukka","correspondingAuthor":false,"prefix":"","firstName":"Ojike","middleName":"","lastName":"Onyekwere","suffix":""},{"id":641504270,"identity":"9bf8e478-4ca4-40e2-923a-f5f534ac422f","order_by":2,"name":"Ozoemena Ani","email":"","orcid":"","institution":"University of Nigeria Nsukka","correspondingAuthor":false,"prefix":"","firstName":"Ozoemena","middleName":"","lastName":"Ani","suffix":""}],"badges":[],"createdAt":"2026-04-16 08:40:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9435489/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9435489/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109444768,"identity":"c33052b2-7421-4a73-8cce-a8fc84773f44","added_by":"auto","created_at":"2026-05-18 08:03:17","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":45780,"visible":true,"origin":"","legend":"\u003cp\u003e3.1: Computed Solar exergy in components (W per plant) across N/P treatment levels (T1-T4).\u003c/p\u003e","description":"","filename":"31.png","url":"https://assets-eu.researchsquare.com/files/rs-9435489/v1/708c6d9fbe9d941e04b5cc3b.png"},{"id":109759605,"identity":"3311d58d-8db6-418a-9019-d29bcebdd644","added_by":"auto","created_at":"2026-05-22 07:27:25","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":46831,"visible":true,"origin":"","legend":"\u003cp\u003e3.3: Computed exergy Reflected components (W per plant) across N/P treatment levels (T1-T4).\u003c/p\u003e","description":"","filename":"33.png","url":"https://assets-eu.researchsquare.com/files/rs-9435489/v1/a686c87bccea458eb2aaf8e2.png"},{"id":109760057,"identity":"e06f1e29-fbcc-4ba9-8520-65a77e5ce4cb","added_by":"auto","created_at":"2026-05-22 07:28:06","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":42175,"visible":true,"origin":"","legend":"\u003cp\u003e3.4: Computed exergy chemical components (W per plant) across N/P treatment levels (T1-T4).\u003c/p\u003e","description":"","filename":"34.png","url":"https://assets-eu.researchsquare.com/files/rs-9435489/v1/c6b5c73aae94a69b70251dce.png"},{"id":109444769,"identity":"38da147f-1658-444b-96ec-f0077b00d1d8","added_by":"auto","created_at":"2026-05-18 08:03:17","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":44099,"visible":true,"origin":"","legend":"\u003cp\u003e3.5: Computed exergy destroyed components (W per plant) across N/P treatment levels (T1-T4).\u003c/p\u003e","description":"","filename":"35.png","url":"https://assets-eu.researchsquare.com/files/rs-9435489/v1/bd1adc2c14969a0750b15bc8.png"},{"id":109759214,"identity":"141f6bcf-7a78-4d04-a7e7-1e518aece012","added_by":"auto","created_at":"2026-05-22 07:26:09","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":93664,"visible":true,"origin":"","legend":"\u003cp\u003e3.6 (a) Exergy performance index (b) Stress index analysis\u003c/p\u003e","description":"","filename":"36.png","url":"https://assets-eu.researchsquare.com/files/rs-9435489/v1/4bd1d604f142695fd541a96f.png"},{"id":109759296,"identity":"651f60c2-02cc-42b2-b0ce-e58ed7473365","added_by":"auto","created_at":"2026-05-22 07:26:31","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":381887,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9435489/v1/e92e433a-11ef-46c3-b06b-82cafed8cf33.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eApplication of the non-zero entropy, finite-area solar exergy model for thermodynamic characterization of Nitrogen and phosphorus nutrient stress in greenhouse-grown cucumber (\u003cem\u003ecucumis sativus\u003c/em\u003e)\u003c/p\u003e","fulltext":[{"header":"1.0 Introduction","content":"\u003cp\u003eNitrogen (N) and phosphorus (P) are the two most agronomically critical macronutrients governing photosynthetic enzyme synthesis, chlorophyll formation, electron transport efficiency, and biomass accumulation in vegetable crops. Their deficiency in commercial cucumber (Cucumis sativus L.) production suppresses Rubisco activity, reduces chlorophyll content, impairs stomatal regulation, and ultimately collapses photosynthetic productivity all of which manifest observably as elevated canopy temperature, reduced leaf area, stunted growth, and diminished yield (Evans \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1989\u003c/span\u003e). Early detection of these deficiencies is therefore a central challenge in precision agriculture, where the goal is to enable targeted, site-specific fertilizer intervention before irreversible yield losses occur. Existing nutrient stress detection approaches spectral indices, visual assessment, tissue analysis, chlorophyll fluorometry, and thermal infrared (TIR) imaging identify stress symptoms without providing a physically grounded explanation of the thermodynamic mechanisms driving the observed canopy thermal responses (Islam et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Pineda et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). This limitation restricts the predictive capability and mechanistic interpretability of current diagnostic frameworks. TIR imaging, in particular, captures canopy temperature anomalies that correlate empirically with nutrient stress, but the causal thermodynamic pathway from nutrient deficiency to photosynthetic inefficiency to entropy generation to canopy temperature elevation remains unquantified in the precision agriculture literature (Messina and Modica \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Zhou et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eExergy analysis, grounded in the Second Law of Thermodynamics, offers a fundamentally different diagnostic paradigm. Unlike energy-based accounting, which conserves quantity, exergy analysis quantifies the quality of energy flows specifically, the fraction of incident solar radiation that is converted to useful biochemical work (biomass) versus irreversibly dissipated as heat. The exergy destruction principle predicts that nutrient-stressed plants, unable to sustain efficient photosynthetic apparatus assembly, generate increased entropy and exhibit elevated canopy temperatures relative to unstressed controls. This principle has been theoretically established and partially supported in corn (Zea mays L.) by Lawrence et al. (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), who demonstrated statistically significant inverse correlations between nitrogen supply rate and canopy temperature consistent with the exergy destruction framework. However, no prior study has applied a fully resolved exergy balance computing all exergy flow components including solar input, emitted, reflected, chemical, and destruction terms under a replicated, multi-level N/P treatment gradient in any vegetable crop.\u003c/p\u003e \u003cp\u003eThe non-zero-entropy, finite-area solar exergy model (Model 2), derived by Kabelac (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1994\u003c/span\u003e) and subsequently applied to crop systems by Alzaben and Fraser (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), provides a physically rigorous and computationally tractable framework for this analysis. Model 2 assumes non zero internal entropy production (consistent with the Carnot reversible engine analogy) and a finite canopy surface area, enabling calculation of solar exergy input as a function of canopy temperature, leaf area, and incident irradiance. It has been identified as the most appropriate model for controlled greenhouse applications where boundary conditions are stable and canopy temperature is the primary thermodynamic state variable (Alzaben and Fraser \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Bararzadeh Ledari et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThis paper presents the first experimental application of Model 2 to characterize exergy flows across a four-level N/P treatment gradient in greenhouse-grown cucumber, with the following specific objectives: (1) compute all exergy balance components (Xsolar,in, Xemitted, Xreflected, Xchemical, Xdes) for each treatment level, (2) derive and evaluate the exergy performance index (ΨX) and normalized stress index as thermodynamic diagnostic metrics, (3) validate Model 2 through polynomial regression analysis of canopy temperature against exergy efficiency across the full treatment and temporal gradient; and (4) establish exergy-based nutrient stress classification thresholds for precision agriculture applications in cucumber production.\u003c/p\u003e"},{"header":"2.0 Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Experimental site and greenhouse conditions\u003c/h2\u003e \u003cp\u003eThe experiment was conducted in a glass-covered greenhouse at the University of Nigeria, Nsukka (6.23\u0026deg;E, 7.35\u0026deg;N, elevation 447 m), located in the humid tropical zone with pronounced wet-season conditions. The greenhouse (13.7 m \u0026times; 7.6 m \u0026times; 3.5 m, L\u0026times;W\u0026times;H) was equipped with natural roof-vent ventilation, drip irrigation for uniform water delivery, and LED supplemental lighting for cloudy-day photosynthetically active radiation (PAR) maintenance. Environmental conditions were maintained within the following ranges; daytime temperature 25\u0026ndash;35\u0026deg;C, relative humidity 60\u0026ndash;70%, PAR 800\u0026ndash;1 500 \u0026micro;mol\u0026middot;m⁻\u0026sup2;\u0026middot;s⁻\u0026sup1;, and soil moisture at 60\u0026ndash;90% of field capacity.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Plant material, experimental design, and nutrient treatments\u003c/h2\u003e \u003cp\u003eCucumber (Cucumis sativus L.) was selected as the experimental species due to its demonstrated high sensitivity to N/P deficiency, economically significant greenhouse production status, and well characterized thermal stress responses (Islam et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2024\u003c/span\u003e, Nikolaou et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Cucumber (\u003cem\u003eCucumis sativus\u003c/em\u003e L.) seeds were obtained from department of crop science University of Nigeria Nsukka (variety: Marketmore 76). The greenhouse experimental site was located at the University of Nigeria, Nsukka (coordinates: 6.23\u0026deg;E, 7.35\u0026deg;N; elevation 447 m). No wild collection occurred. A Randomized Complete Block Design (RCBD) was adopted, comprising 48 plants distributed across four spatial blocks (A - D), each containing four nutrient treatment replicates (n\u0026thinsp;=\u0026thinsp;3 plants per treatment per block). Block assignment controlled for microenvironmental variation in light and temperature within the greenhouse. Treatments were randomly assigned within each block with weekly positional rotation to minimize microclimate bias. Four nitrogen and phosphorus treatment levels were applied through fertigation (calcium ammonium nitrate and urea in drip irrigation water) throughout the 44day experimental period as described in Table\u0026nbsp;1.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2.1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eNutrient treatment levels and physiological interpretation.\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=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTreatment\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eN/P Level (mg\u0026middot;kg⁻\u0026sup1;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStress Category\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePhysiological Rationale\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e120/40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOptimal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFull photosynthetic apparatus capacity, reference condition\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e80/30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eModerate Stress\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e67% of optimal N, early chlorophyll and Rubisco reduction\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40/20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSevere Stress\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e33% of optimal N, substantial photosynthetic impairment\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0/10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExtreme Deficiency\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eZero N supply, near-complete photosynthetic collapse\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003eNote: N/P levels expressed as mg\u0026middot;kg⁻\u0026sup1; substrate dry weight. All other macro- and micro-nutrients were supplied at agronomically optimal levels across all treatments.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Thermal imaging and canopy temperature acquisition\u003c/h2\u003e \u003cp\u003eCanopy temperatures were acquired every four days over the 44day monitoring period (12 measurement occasions: Days 1, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44)\u003c/p\u003e \u003cp\u003eusing a UTi120s professional thermal imager (120\u0026times;90 pixel resolution, spectral range 7.5\u0026ndash;14 \u0026micro;m, emissivity ε\u0026thinsp;=\u0026thinsp;0.95, accuracy\u0026thinsp;\u0026plusmn;\u0026thinsp;2\u0026deg;C per manufacturer specification, UTi Technology Co. Ltd, Shenzhen, China). All images were captured at a fixed height of 20 cm above the leaf surface, with a consistent 45\u0026ndash;90\u0026deg; incidence angle to minimize reflection errors. Measurements were conducted between 11:00 and 14:00 to maximize canopy-to-air temperature differentiation under peak irradiance. Instrument accuracy was validated against a calibrated type-K thermocouple (\u0026plusmn;\u0026thinsp;0.5\u0026deg;C) on five representative plant surfaces at Days 8, 24, and 40, yielding a mean absolute error of \u0026le;\u0026thinsp;1\u0026deg;C across 15 paired measurements. Thermal images were processed in MATLAB R2018B (MathWorks Inc.) using the Image Processing Toolbox. For each plant, a region of interest (ROI) was manually delineated excluding pixels within 5 mm of the pot edge and any pixel deviating more than\u003c/p\u003e \u003cp\u003e3\u0026deg;C from the canopy mean, to eliminate non-canopy contamination. Mean ROI canopy temperature (Ts) was extracted for all downstream exergy calculations. Atmospheric correction was not applied as measurements were conducted under controlled greenhouse conditions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Computation of exergy balance components\u003c/h2\u003e \u003cp\u003eEach cucumber plant canopy is modelled as a finite-area, open thermodynamic control volume. The exergy balance under quasi-steady-state conditions is shown in Eq.\u0026nbsp;2.1.\u003c/p\u003e \u003cp\u003eX\u003csub\u003ein\u003c/sub\u003e = X\u003csub\u003eout\u003c/sub\u003e + X\u003csub\u003edes\u003c/sub\u003e (2.1)\u003c/p\u003e \u003cp\u003ewhere the total exergy input Xin is the incident solar exergy Xsolarin, and the total exergy output Xout comprises three terms as seen in Eq.\u0026nbsp;2.2.\u003c/p\u003e \u003cp\u003eX\u003csub\u003eout\u003c/sub\u003e = X\u003csub\u003eemitted\u003c/sub\u003e + X\u003csub\u003ereflected\u003c/sub\u003e + X\u003csub\u003echemical\u003c/sub\u003e (2.2)\u003c/p\u003e \u003cp\u003eExergy destruction X\u003csub\u003edes\u003c/sub\u003e is therefore shown in Eq.\u0026nbsp;2.3.\u003c/p\u003e \u003cp\u003eX\u003csub\u003edes\u003c/sub\u003e = X\u003csub\u003esolar,in\u003c/sub\u003e \u0026minus; (X\u003csub\u003eemitted\u003c/sub\u003e + X\u003csub\u003ereflected\u003c/sub\u003e + X\u003csub\u003echemical\u003c/sub\u003e) (2.3)\u003c/p\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.4.1 Solar exergy input (X\u003csub\u003esolar,in\u003c/sub\u003e)\u003c/h2\u003e \u003cp\u003eSolar exergy input was computed using the Model 2 formulation (Eq.\u0026nbsp;2.4) as:\u003c/p\u003e \u003cp\u003eXsolarin\u0026thinsp;=\u0026thinsp;A \u0026times; G \u0026times; [1 \u0026minus; (4/3)(Ts/Tsun) + (1/3)(Ts/Tsun)⁴] (2.4)\u003c/p\u003e \u003cp\u003e \u003cem\u003eWhere;\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eA is the effective photosynthetically active leaf area (m\u0026sup2;)\u003c/em\u003e,\u003c/p\u003e \u003cp\u003e \u003cem\u003eG is the measured incident solar irradiance (Wm⁻\u0026sup2;)\u003c/em\u003e,\u003c/p\u003e \u003cp\u003e \u003cem\u003eTs is the canopy surface temperature in Kelvin, and\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eTsun\u0026thinsp;=\u0026thinsp;5 778 K (Eq.\u0026nbsp;2.4).\u003c/em\u003e \u003c/p\u003e \u003cp\u003eLeaf area per plant was estimated non-destructively using the length-width-correction factor method: LA\u0026thinsp;=\u0026thinsp;L \u0026times; W \u0026times; k, where k\u0026thinsp;=\u0026thinsp;0.75 for broadleaf geometries, validated against a scanned leaf subset at harvest. Incident irradiance was maintained at a controlled 800 W\u0026middot;m⁻\u0026sup2; throughout the experiment.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e2.4.2 Emitted exergy (X\u003csub\u003eemitted\u003c/sub\u003e)\u003c/h2\u003e \u003cp\u003eExergy of longwave thermal radiation emitted by the canopy was computed using the Stefan\u0026ndash;Boltzmann relationship with a Carnot efficiency correction using Eq.\u0026nbsp;2.5.\u003c/p\u003e \u003cp\u003eX\u003csub\u003eemitted\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;ε\u0026thinsp;\u0026times;\u0026thinsp;σ\u0026thinsp;\u0026times;\u0026thinsp;A \u0026times; (Ts⁴ \u0026minus; Ta⁴) \u0026times; (1\u0026thinsp;\u0026minus;\u0026thinsp;Ta/Ts) (2.5)\u003c/p\u003e \u003cp\u003ewhere ε\u0026thinsp;=\u0026thinsp;0.95 (canopy emissivity), σ\u0026thinsp;=\u0026thinsp;5.67 \u0026times; 10⁻⁸ W\u0026middot;m⁻\u0026sup2;\u0026middot;K⁻⁴, Ts is canopy temperature and Ta is ambient air temperature, both in Kelvin (Alzaben and Fraser \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e2.4.3 Reflected exergy (X\u003csub\u003ereflected\u003c/sub\u003e)\u003c/h2\u003e \u003cp\u003eExergy of reflected shortwave solar radiation was calculated using Eq.\u0026nbsp;2.6\u003c/p\u003e \u003cp\u003eX\u003csub\u003ereflected\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;α\u0026thinsp;\u0026times;\u0026thinsp;G \u0026times; A\u0026thinsp;\u0026times;\u0026thinsp;ϕsolar (2.6)\u003c/p\u003e \u003cp\u003e \u003cem\u003eWhere;\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eα is the effective canopy albedo (reflectance coefficient) and\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eϕsolar\u0026thinsp;=\u0026thinsp;0.93 is the solar exergy factor derived from the Model 2 formulation at ambient temperature conditions\u003c/em\u003e (Kabelac \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1994\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e2.4.4 Chemical exergy (Xchemical)\u003c/h2\u003e \u003cp\u003eThe chemical exergy stored in net biomass accumulation was computed using Eq.\u0026nbsp;2.7.\u003c/p\u003e \u003cp\u003eX\u003csub\u003echemical\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;Δm \u0026times; bbio (2.7)\u003c/p\u003e \u003cp\u003e \u003cem\u003eWhere;\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eΔm (kg) is the net dry biomass increment measured gravimetrically and\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003ebbio\u0026thinsp;=\u0026thinsp;18.7 MJ\u0026middot;kg⁻\u0026sup1; is the standard specific chemical exergy of plant dry matter\u003c/em\u003e, consistent with the elemental-composition-based estimates established in the literature for C3 crops (Righetto and Mady \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2023\u003c/span\u003e, Silva et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Biomass gain was measured at weekly intervals using a calibrated digital balance (0.01 g resolution) after oven-drying at 60\u0026deg;C for 48 h.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e2.4.5 Exergy destruction metrices\u003c/h2\u003e \u003cp\u003eExergy destruction was derived from the balance equation (Eq.\u0026nbsp;2.3) and further described using Eq.\u0026nbsp;2.8\u003c/p\u003e \u003cp\u003eX\u003csub\u003edes\u003c/sub\u003e = T\u003csub\u003e₀\u003c/sub\u003e x S\u003csub\u003egen\u003c/sub\u003e (2.8)\u003c/p\u003e \u003cp\u003e \u003cem\u003eWhere;\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eX\u003c/em\u003e \u003csub\u003e \u003cem\u003edes\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e(W) is the exergy destruction rate and\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003eSgen (W\u0026middot;K⁻\u0026sup1;) is the rate of entropy generation within the control volume\u003c/em\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Exergy performance index and stress quantification\u003c/h2\u003e \u003cp\u003eTo facilitate quantitative comparison across treatments, a relative exergy performance index ΨX was computed using Eq.\u0026nbsp;2.9.\u003c/p\u003e \u003cp\u003eΨX\u0026thinsp;=\u0026thinsp;1 \u0026minus; (X\u003csub\u003edes\u003c/sub\u003e / X\u003csub\u003ein\u003c/sub\u003e) (2.9)\u003c/p\u003e \u003cp\u003eThis dimensionless index, bounded between 0 and 1, represents the fraction of incoming solar exergy not destroyed by irreversibility within the plant system. A normalised thermodynamic stress index is then derived as shown in Eq.\u0026nbsp;2.10.\u003c/p\u003e \u003cp\u003eStress Index = (ΨX\u003csub\u003eopt\u003c/sub\u003e\u0026thinsp;\u0026minus;\u0026thinsp;ΨX\u003csub\u003etreatment\u003c/sub\u003e) / ΨX\u003csub\u003eopt\u003c/sub\u003e (2.10)\u003c/p\u003e \u003cp\u003e \u003cem\u003eWhere;\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eΨX\u003c/em\u003e \u003csub\u003e \u003cem\u003eopt\u003c/em\u003e \u003c/sub\u003e \u003cem\u003eis the performance index under optimal nutrient conditions (T1).\u003c/em\u003e\u003c/p\u003e \u003cp\u003eThis index ranges from 0 (no stress) to 1 (maximum stress within the experimental range) and enables objective, dimensionless comparison of thermodynamic degradation across treatments (Fraser and Kay \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2004\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e2.6 Statistical Analysis\u003c/h2\u003e \u003cp\u003ePolynomial (second-order) regression analysis was employed to model the relationship between canopy temperature (independent variable) and exergy efficiency (dependent variable, defined as ηex\u0026thinsp;=\u0026thinsp;1\u0026thinsp;\u0026minus;\u0026thinsp;Ta/Ts) over the 44day monitoring period (n\u0026thinsp;=\u0026thinsp;12 time points per treatment). Separate regression models were fitted for each nutrient treatment. Model performance was evaluated using the coefficient of determination (R\u0026sup2;) and root mean square error (RMSE). Analysis of variance (ANOVA) was applied to each regression to test statistical significance at the α\u0026thinsp;=\u0026thinsp;0.05 level. All analyses were performed in MATLAB R2018B using the polyfit, polyval, and anovan functions. The level of significance is indicated using standard abbreviations (** p\u0026thinsp;\u0026lt;\u0026thinsp;0.01; * p\u0026thinsp;\u0026lt;\u0026thinsp;0.05).\u003c/p\u003e \u003c/div\u003e"},{"header":"3.0 Results","content":"\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Measured primary parameters and morphological responses\u003c/h2\u003e \u003cp\u003eThe progressive nutrient limitation resulted in measurable and monotonic changes in all primary plant parameters as shown in Table \u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e.\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 3.1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMeasured primary morphological and thermal parameters across N/P treatments (normalized to plant control volume, Day 32\u0026ndash;44 mature canopy phase).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\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 \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTreatment\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLeaf Area A (m\u0026sup2;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCanopy Temp Ts (K)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAlbedo α\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBiomass Gain (kg)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT1 (Optimal: 120/40)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0125\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT2 (Moderate: 80/30)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e303\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0092\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT3 (Severe: 40/20)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e307\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0054\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT4 (Extreme: 0/10)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e311\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0021\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\u003eTs: mean canopy surface temperature during measurement period; ambient air temperature Ta\u0026thinsp;=\u0026thinsp;298 K across all treatments.\u003c/p\u003e \u003cp\u003eFrom Table \u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e, Leaf area declined from 0.48 m\u0026sup2; (T1, optimal) to 0.32 m\u0026sup2; (T4, zero nitrogen), representing a 33% structural reduction driven by nitrogen's essential role in governing cell division and meristematic activity. Canopy temperature increased correspondingly from 300 K (T1) to 311 K (T4), reflecting the impairment of transpirational cooling as photosynthetic and stomatal regulatory capacity declined (Pineda et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Nikolaou et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Canopy albedo increased modestly from 0.18 (T1) to 0.26 (T4), consistent with chlorophyll degradation reducing light absorption efficiency. Biomass gain exhibited the most pronounced decline, from 0.0125 kg (T1) to 0.0021 kg (T4) reduction directly attributable to collapsed photosynthetic carbon fixation capacity (Evans \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1989\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Exergy balance analysis\u003c/h2\u003e \u003cp\u003eThe results of exergy balance analysis are shown in Table \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3.2\u003c/span\u003e. All the values represent mean exergy fluxes computed for the mature canopy phase. (G\u0026thinsp;=\u0026thinsp;800 Wm⁻\u0026sup2;, Ta\u0026thinsp;=\u0026thinsp;298 K, ε\u0026thinsp;=\u0026thinsp;0.95, ϕsolar\u0026thinsp;=\u0026thinsp;0.93)\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 3.2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComputed exergy balance components (W per plant) across N/P treatment levels.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\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 \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTreatment\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eXsolar,in (W)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eXemitted (W)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eXreflected (W)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eXchemical (W)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eXout (W)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eXdes (W)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT1 (Optimal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e357\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e234\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e340\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT2 (Moderate)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e334\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e172\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT3 (Severe)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e289\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e101\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e263\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e66\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT4 (Extreme)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e235\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e138\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e239\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e112\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1 Solar exergy input (X\u003csub\u003esolarin\u003c/sub\u003e)\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSolar exergy input decreased monotonically from 357 W (T1) to 235 W (T4), a 34% reduction (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3.2\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e). This decline is attributable exclusively to the progressive reduction in effective photosynthetically active leaf area under nutrient stress, as incident irradiance was maintained constant at 800 W\u0026middot;m⁻\u0026sup2; throughout the experiment. The intermediate treatments showed proportional intermediate reductions (T2\u0026thinsp;=\u0026thinsp;334 W; T3\u0026thinsp;=\u0026thinsp;289 W), establishing a clear morphological - exergetic coupling: nutrient availability governs canopy architecture, which in turn determines the fundamental energy budget entering the plant system.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e4.2.2 Emitted exergy (Xemitted)\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eEmitted exergy exhibited the most dramatic response to nutrient stress, increasing 3.3-fold from 42 W (T1) to 138 W (T4), with intermediate values of T2\u0026thinsp;=\u0026thinsp;61 W and T3\u0026thinsp;=\u0026thinsp;96 W (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3.2\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3.2\u003c/span\u003e). This non-linear escalation reflects the T\u003csub\u003e4\u003c/sub\u003e dependence of radiative heat transfer: the canopy temperature increase of 11 K from T1 to T4 (300\u0026ndash;311 K) is amplified by the quartic relationship into a disproportionately large radiative exergy signal (Kabelac \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1994\u003c/span\u003e). Under optimal nutrition, robust transpiration driven by high photosynthetic activity maintains canopy temperature near ambient through evaporative cooling. As nitrogen limitation reduces photosynthetic capacity, transpiration rates decline, stomatal conductance decreases (Nikolaou et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), and leaf surface temperature rises dramatically increasing the radiative exergy dissipated to the environment.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section3\"\u003e \u003ch2\u003e4.2.3 Reflected exergy (Xreflected)\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eReflected exergy remained relatively invariant across all treatments, ranging from 62 to 67 W with a coefficient of variation of only 3.4% ((Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3.2\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3.3\u003c/span\u003e). This constancy is mechanistically significant: it demonstrates that the primary exergetic failure under nutrient stress is metabolic and thermal rather than optical. Proportional reflectance increased from 17.9% (T1: 64/357 W) to 26.4% (T4: 62/235 W), however, indicating that while absolute reflectance is stable, a larger fraction of the reduced exergy budget is returned to the environment via reflection under severe stress.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section3\"\u003e \u003ch2\u003e4.2.4 Chemical exergy (Xchemical)\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eChemical exergy showed the most fundamental decline across treatments, decreasing from 234 W (T1) to 39 W (T4) an 83% reduction representing the near-complete collapse of the plant's primary energy conversion function (Table \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3.2\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e3.4\u003c/span\u003e). Intermediate treatments showed proportional degradation (T2\u0026thinsp;=\u0026thinsp;172 W; T3\u0026thinsp;=\u0026thinsp;101 W). Mechanistically, this decline directly reflects nitrogen's indispensable role as the central atom of chlorophyll and as a component of Rubisco, P700, P680, and cytochrome-b/c electron transport complexes (Evans \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1989\u003c/span\u003e; Bararzadeh Ledari et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Reducing nitrogen availability therefore simultaneously impairs light absorption, electron transport rate, and carbon fixation capacity a concerted collapse of the entire photosynthetic exergy conversion apparatus.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section3\"\u003e \u003ch2\u003e4.2.5 Exergy destruction (X\u003csub\u003edes\u003c/sub\u003e)\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eExergy destruction increased from 17 W (T1) to 112 W (T4) ((Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3.2\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e3.5\u003c/span\u003e)), a six-fold escalation, exhibiting the largest proportional change of any exergy balance component and showing a roughly exponential progression: T1\u0026thinsp;=\u0026thinsp;17 W; T2\u0026thinsp;=\u0026thinsp;34 W (2.0\u0026times;); T3\u0026thinsp;=\u0026thinsp;66 W (3.9\u0026times;); T4\u0026thinsp;=\u0026thinsp;112 W (6.6\u0026times;). The symmetry between the 6.6-fold decrease in chemical exergy and the 6.6-fold increase in exergy destruction is physically non-coincidental: it directly expresses the Second Law energy not captured in biomass must be dissipated through entropy-generating irreversibilities (Fraser and Kay \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). Mechanistic sources of accelerating exergy destruction under nutrient stress include: non-photochemical quenching of excess absorbed photons as thermal dissipation; disruption of metabolic pathway flux creating futile cycles with high entropy production; increased baseline respiration-to-photosynthesis ratio; and viscous dissipation from osmolyte synthesis under incipient water stress accompanying nutrient limitation.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Exergy performance index and normalized stress analysis\u003c/h2\u003e \u003cp\u003eThe exergy performance index (ΨX) declined systematically from 0.952 (T1) to 0.523 (T4), representing a 45% relative decline in Second Law efficiency (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e3.3\u003c/span\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 3.3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExergy performance indicators across N/P treatment levels.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTreatment\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eX\u003csub\u003edes\u003c/sub\u003e (W)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eΨX\u0026thinsp;=\u0026thinsp;1\u0026minus;(X\u003csub\u003edes\u003c/sub\u003e/X\u003csub\u003ein\u003c/sub\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStress index\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eClassification\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT1 (Optimal: 120/40)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.952\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAdequate/Optimal\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT2 (Moderate: 80/30)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.898\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eModerate Stress\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT3 (Severe: 40/20)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.772\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.189\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSevere Stress\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT4 (Extreme: 0/10)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e112\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.523\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCritical Deficiency\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\u003eFrom Table \u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e3.3\u003c/span\u003e, this degradation reflects two concurrent effects; diminished input exergy due to reduced leaf area (34% decrease) and dramatically increased exergy destruction. The T1 value (ΨX\u0026thinsp;=\u0026thinsp;0.952) indicates operation near theoretical reversibility, consistent with evolutionary optimization of the photosynthetic apparatus for minimal entropy production under adequate nutrient supply. The T4 value (ΨX\u0026thinsp;=\u0026thinsp;0.523) indicates severely compromised efficiency, with the system dissipating nearly double the exergetic fraction per unit input compared to optimal conditions.\u003c/p\u003e \u003cp\u003eThe normalized stress index (Table \u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e3.3\u003c/span\u003e, Fig.\u0026nbsp;3.6b) progressed as 0.000 (T1), 0.057 (T2), 0.189 (T3), and 0.450 (T4), revealing a non-linear, approximately exponential relationship between nutrient limitation intensity and thermodynamic degradation. The accelerating increments (0.057, 0.132, 0.261) demonstrate that early-stage stress (T2) causes modest efficiency loss (5.7% of maximum stress), while severe stress (T3, T4) causes disproportionately large efficiency collapse consistent with threshold-based physiological responses characteristic of biological systems where nutrient concentration below critical levels triggers cascading failures in photosynthetic apparatus assembly.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Validation (polynomial regression of canopy temperature against exergy efficiency)\u003c/h2\u003e \u003cp\u003ePolynomial (second-order) regression analysis of canopy temperature versus exergy efficiency yielded statistically significant relationships across all four nutrient treatments, satisfying the predefined validation criteria (Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e3.4\u003c/span\u003e). R\u0026sup2; values ranged from 0.668 (T1, optimal) to 0.506 (T4, extreme deficiency), with all models significant at p\u0026thinsp;\u0026lt;\u0026thinsp;0.05.\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 3.4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eANOVA results for polynomial regression of canopy temperature versus exergy efficiency across N/P treatments.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\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 \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTreatment\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eR\u0026sup2;\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAdj. R\u0026sup2;\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eF-stat\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSignificance\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT1 (Optimal)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.668\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.602\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT2 (Moderate)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.641\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.569\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT3 (Severe)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.582\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.498\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT4 (Extreme)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.506\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.407\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e*\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\u003e** p\u0026thinsp;\u0026lt;\u0026thinsp;0.01; * p\u0026thinsp;\u0026lt;\u0026thinsp;0.05; n\u0026thinsp;=\u0026thinsp;12 time points per treatment; DF regression\u0026thinsp;=\u0026thinsp;2; DF residual\u0026thinsp;=\u0026thinsp;9. RMSE units: \u0026times;10⁻\u0026sup3; exergy efficiency.\u003c/p\u003e \u003cp\u003eUnder optimal nutrition (T1: R\u0026sup2; = 0.668, F\u0026thinsp;=\u0026thinsp;8.46, p\u0026thinsp;=\u0026thinsp;0.008), the regression achieved the strongest coupling, indicating that approximately two-thirds of exergy efficiency variation is thermally explained even when plants are physiologically resilient. Under moderate stress (T2: R\u0026sup2; = 0.641, F\u0026thinsp;=\u0026thinsp;7.91, p\u0026thinsp;=\u0026thinsp;0.011), the slight decrease in coupling strength (4.1 percentage points from T1) reflects emerging but not yet dominant physiological constraint. This treatment represents the operationally optimal diagnostic window: thermal efficiency coupling is strong (R\u0026sup2; \u0026gt; 0.64) and the stress is still reversible with targeted fertilizer intervention. Under severe stress (T3: R\u0026sup2; = 0.582, F\u0026thinsp;=\u0026thinsp;6.25, p\u0026thinsp;=\u0026thinsp;0.020) and extreme deficiency (T4: R\u0026sup2; = 0.506, F\u0026thinsp;=\u0026thinsp;5.14, p\u0026thinsp;=\u0026thinsp;0.033), coupling strength declines progressively as metabolic instability increases and canopy temperature converges near-maximum values with reduced variance, limiting the discriminatory power of the thermal signal. The systematic decline in R\u0026sup2; (16.2 percentage-point total decrease across the treatment gradient) establishes a critical practical principle; TIR-based exergy diagnostics are most reliable and actionable for early-to-moderate stress detection.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003e4.5 Proposed exergy-based nutrient stress classification\u003c/h2\u003e \u003cp\u003eBased on the exergy efficiency ranges observed during the mature canopy phase (Days 32\u0026ndash;44) and corroborated by the ΨX values, the following thermodynamically derived nutrient status classification thresholds are proposed for greenhouse cucumber (Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e3.5\u003c/span\u003e)\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 3.5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExergy efficiency-based nutrient stress classification thresholds for greenhouse cucumber.\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=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExergy performance index (ΨX) range\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNutrient status classification / Recommended management action\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eΨX\u0026thinsp;\u0026gt;\u0026thinsp;0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAdequate to Optimal: No intervention required\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eΨX\u0026thinsp;=\u0026thinsp;0.77\u0026ndash;0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModerate Stress: Monitor closely; consider targeted N/P supplementation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eΨX\u0026thinsp;=\u0026thinsp;0.55\u0026ndash;0.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSevere Stress: Fertilizer intervention required; yield penalty likely\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eΨX\u0026thinsp;\u0026lt;\u0026thinsp;0.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCritical Deficiency: Immediate corrective treatment necessary; high yield loss risk\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4.0 Conclusion","content":"\u003cp\u003eThis study provides a rigorous thermodynamic interpretation of nitrogen and phosphorus (N/P) nutrient stress in cucumber by integrating exergy analysis with thermal infrared diagnostics. The results demonstrate that nutrient stress is fundamentally a manifestation of reduced thermodynamic efficiency and increased irreversibility within the plant system, consistent with the First and Second Laws of Thermodynamics (Fraser and Kay, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Bararzadeh Ledari et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). A major outcome is the inverse symmetry between chemical exergy and exergy destruction, both varying by a factor of 6.6 across treatments, confirming that reductions in biomass energy storage are directly dissipated as entropy. The increase in emitted exergy shows the diagnostic strength of thermal infrared imaging, where small canopy temperature elevations are amplified through T\u003csub\u003e4\u003c/sub\u003e radiative scaling, providing a sensitive indicator of physiological inefficiency. The stability of reflected exergy (CV\u0026thinsp;=\u0026thinsp;3.4%) further confirms that stress-induced failure occurs within the photosynthetic conversion system rather than canopy structure. Nitrogen/phosphorus were identified as the dominant regulator of photosynthetic exergy conversion, with an 83% reduction in chemical exergy linked to its biochemical role in chlorophyll, Rubisco, and electron transport systems (Evans, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1989\u003c/span\u003e; Bararzadeh Ledari et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Model validation showed statistically significant thermal-efficiency coupling (R\u0026sup2; = 0.506\u0026ndash;0.668; p\u0026thinsp;\u0026lt;\u0026thinsp;0.05), with stronger predictive capability under early-to-moderate stress, establishing this range as the optimal intervention window. Compared with prior studies (Lawrence et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Alzaben and Fraser, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), this work advances the field through full exergy balance validation, dual nutrient stress analysis, and experimentally derived diagnostic thresholds. Therefore, this study confirms exergy destruction as the most sensitive stress indicator, establishes dimensionless performance indices for decision support, and demonstrates that thermal imaging, when grounded in exergy theory, provides a mechanistic and scalable tool for precision agriculture nutrient management.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eC.G.U.: Conceptualization, Methodology, Data Collection, Formal Analysis, Writing Original Draft. O.A.: Supervision, Writing Review and Editing. O.O.: Supervision, Writing Review and Editing. All authors have read and agreed to the published version of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research was not supported no funded by any institution.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict Of interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePermissions for plant collection:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe cucumber seeds used in this study were commercially purchased/cultivated at the University of Nigeria Nsukka greenhouse facility (institution-owned land). No collection from government-owned land, private farmland, or protected areas was conducted. Therefore, no specific permits or licences were required. All activities complied with institutional research policies.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets generated and analyzed during the current study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgment\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe acknowledge with profound gratitude the authors whose work were cited or paraphrased in this report.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to publish declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to participate declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable. this study did not involve human participants, human data, human tissue, or animal subjects requiring ethical approval. This study involved cultivated cucumber plants (cucumis sativus l.), which are neither endangered nor protected species. no wild collection was performed. all plant handling complied with institutional guidelines of the university of Nigeria, Nsukka, and with local and national agricultural research regulations of Nigeria. no specific ethical approval was required for this study.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAlzaben H, Fraser R. Energy and exergy analyses applied to a crop plant system. Thermo. 2025;5:3. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/thermo5010003\u003c/span\u003e\u003cspan address=\"10.3390/thermo5010003\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBararzadeh Ledari M, Saboohi Y, Valero A, Azamian S. 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Comput Electron Agric. 2021;182:106019. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.compag.2021.106019\u003c/span\u003e\u003cspan address=\"10.1016/j.compag.2021.106019\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"discover-plants","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Plants](https://link.springer.com/journal/44372)","snPcode":"44372","submissionUrl":"https://submission.springernature.com/new-submission/44372/3","title":"Discover Plants","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"exergy analysis, solar exergy model, thermal infrared imaging, nutrient stress, cucumber, precision agriculture","lastPublishedDoi":"10.21203/rs.3.rs-9435489/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9435489/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eConventional nutrient stress diagnostics identify symptoms without explaining the underlying thermodynamic mechanisms. This study presents the first experimental application of the non-zero-entropy, finite-area solar exergy model (Model 2) to characterize nitrogen and phosphorus (N/P) stress in greenhouse-grown cucumber (\u003cem\u003eCucumis-sativus\u003c/em\u003e). A Randomized Complete Block Design comprising 48 plants across four N/P treatment levels T1\u0026thinsp;=\u0026thinsp;120/40 mg\u0026middot;kg⁻\u0026sup1; (optimal), T2\u0026thinsp;=\u0026thinsp;80/30 (moderate), T3\u0026thinsp;=\u0026thinsp;40/20 (severe), T4\u0026thinsp;=\u0026thinsp;0/10 mg\u0026middot;kg⁻\u0026sup1; (extreme deficiency) was conducted over 44days. Canopy temperatures were acquired using a UTi120s thermal imager under 800 Wm⁻\u0026sup2; irradiance. Exergy balance analysis revealed that solar exergy input declined from 357W (T1) to 235W (T4), driven by nutrient-induced leaf area reduction. Emitted exergy increased from 42\u0026ndash;138 W, reflecting T\u003csub\u003e4\u003c/sub\u003e radiative amplification of canopy temperature elevation, while chemical exergy collapsed 83% (234\u0026thinsp;\u0026minus;\u0026thinsp;39 W) and exergy destruction escalated from 17\u0026ndash;112 W. The exergy performance index (ΨX) declined from 0.952 to 0.523 and the normalized stress index increased exponentially (0.000\u0026ndash;0.450). Polynomial regression of canopy temperature against exergy efficiency yielded statistically significant relationships across all treatments (R\u0026sup2; = 0.506\u0026ndash;0.668; p\u0026thinsp;\u0026lt;\u0026thinsp;0.05), confirming early-to-moderate stress as the optimal diagnostic window. Exergy destruction is validated as the most sensitive thermodynamic metric for precision agriculture nutrient stress monitoring.\u003c/p\u003e","manuscriptTitle":"Application of the non-zero entropy, finite-area solar exergy model for thermodynamic characterization of Nitrogen and phosphorus nutrient stress in greenhouse-grown cucumber (cucumis sativus)","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-18 08:03:13","doi":"10.21203/rs.3.rs-9435489/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-05-07T15:25:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"310253267685742617746591612410831796056","date":"2026-05-07T12:42:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"213956749897974866912820880123174850202","date":"2026-05-07T11:31:10+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-05-07T11:07:47+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-05-05T14:41:20+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-28T00:41:24+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Plants","date":"2026-04-28T00:37:30+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-plants","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Plants](https://link.springer.com/journal/44372)","snPcode":"44372","submissionUrl":"https://submission.springernature.com/new-submission/44372/3","title":"Discover Plants","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"068667ab-60c1-4ee7-a2a5-56b91848ffa2","owner":[],"postedDate":"May 18th, 2026","published":true,"recentEditorialEvents":[{"type":"editorInvitedReview","content":"","date":"2026-05-07T15:25:55+00:00","index":22,"fulltext":""},{"type":"reviewerAgreed","content":"310253267685742617746591612410831796056","date":"2026-05-07T12:42:33+00:00","index":21,"fulltext":""},{"type":"reviewerAgreed","content":"213956749897974866912820880123174850202","date":"2026-05-07T11:31:10+00:00","index":20,"fulltext":""},{"type":"reviewersInvited","content":"5","date":"2026-05-07T11:07:47+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-05-05T14:41:20+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-18T08:03:13+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-18 08:03:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9435489","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9435489","identity":"rs-9435489","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}