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The paper describes the Theory of Entropicity (ToE), proposing a unifying field-theoretic framework in which entropy is treated as a fundamental scalar field S(x,t) that generates physical geometry, motion, and dynamics. It argues that statistical metrics from information geometry (Fisher-Rao and Fubini-Study) transform into metric-affine geometries via entropy-driven deformation controlled by the Rényi–Tsallis α–q formalism, using Amari–Čencov α-connections to link informational curvature to spacetime curvature. A key claim is that the entropy field’s dynamics are determined by the “Obidi Action,” producing the “Master Entropic Equation” as an entropic analogue of Einstein’s field equations, with a constitutive relation α = 2(1 − q) connecting non-extensive deformation to affine asymmetry and irreversibility. The paper is a preprint and explicitly notes it has not been peer reviewed, which is a limitation on evidentiary strength. The paper does not explicitly discuss endometriosis or adenomyosis; it was included in the corpus via a keyword match in the upstream search index.
Abstract
The Theory of Entropicity (ToE) presents a unifying mathematical architecture in which entropy is not a secondary statistical construct but the fundamental field generating all physical geometry, motion, and dynamics. This paper offers both a rigorous and intuitive explanation of how ToE fuses thermodynamics, information geometry, and spacetime physics through the Amari-Čencov α-connections, establishing a coherent field-theoretic foundation. Statistical metrics such as the Fisher-Rao and Fubini-Study are shown to transform into physical metric-affine geometries under entropy-driven deformation governed by the Rényi-Tsallis α-q formalism. Within this framework, entropy acts as an ontological scalar field S(x, t) whose dynamics are determined by the Obidi Action, yielding the Master Entropic Equation (MEE) as the entropic analogue of Einstein's field equations. The constitutive relation α = 2(1 − q) mathematically links non-extensive entropy deformation to affine asymmetry, forming the geometric bridge between information flow irreversibility and spacetime curvature. Through this transformation, informational curvature becomes physical curvature, and entropy emerges as the causal fabric that underlies space, time, and matter. Ultimately, the Theory of Entropicity (ToE) extends Einstein's geometric paradigm by embedding gravity, quantum mechanics, and thermodynamics within a single entropic continuum. It provides a comprehensive and elegant field-theoretic structure that interprets the universe as an entropy-governed system, where all physical laws, geometries, and interactions arise naturally from the irreversible flow and curvature of the entropic field itself.
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A Simple Explanation of the Unifying Mathematical Architecture of the Theory of Entropicity (ToE) Crucial Elements of ToE as a Field Theory | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 20 October 2025 V1 Latest version Share on A Simple Explanation of the Unifying Mathematical Architecture of the Theory of Entropicity (ToE) Crucial Elements of ToE as a Field Theory Author : John Onimisi Obidi 0009-0004-3606-3182 [email protected] Authors Info & Affiliations 310 views 143 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract The Theory of Entropicity (ToE) presents a unifying mathematical architecture in which entropy is not a secondary statistical construct but the fundamental field generating all physical geometry, motion, and dynamics. This paper offers both a rigorous and intuitive explanation of how ToE fuses thermodynamics, information geometry, and spacetime physics through the Amari-Čencov α-connections, establishing a coherent field-theoretic foundation. Statistical metrics such as the Fisher-Rao and Fubini-Study are shown to transform into physical metric-affine geometries under entropy-driven deformation governed by the Rényi-Tsallis α-q formalism. Within this framework, entropy acts as an ontological scalar field S(x, t) whose dynamics are determined by the Obidi Action, yielding the Master Entropic Equation (MEE) as the entropic analogue of Einstein's field equations. The constitutive relation α = 2(1 − q) mathematically links non-extensive entropy deformation to affine asymmetry, forming the geometric bridge between information flow irreversibility and spacetime curvature. Through this transformation, informational curvature becomes physical curvature, and entropy emerges as the causal fabric that underlies space, time, and matter. Ultimately, the Theory of Entropicity (ToE) extends Einstein's geometric paradigm by embedding gravity, quantum mechanics, and thermodynamics within a single entropic continuum. It provides a comprehensive and elegant field-theoretic structure that interprets the universe as an entropy-governed system, where all physical laws, geometries, and interactions arise naturally from the irreversible flow and curvature of the entropic field itself. Supplementary Material File (a simple explanation of the unifying mathematical architecture of the theory of entropicity (toe)_v3_s1.pdf) Download 529.58 KB Information & Authors Information Version history V1 Version 1 20 October 2025 DOI 10.22541/au.176099705.55607091/v1 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords affine connections amari-čencov α-connections christoffel symbols constitutive law/relation einstein field equations einstein-hilbert action entropic field entropic geodesics fisher-rao(fr) fubini-study (fs) general relativity (gr) information geometry levi-civita connections metrics of classical and quantum distinguishability obidi action obidi formalism quantum mechanics (qm) rényi entropy thermodynamics tsallis entropy vuli-ndlela integral Authors Affiliations John Onimisi Obidi 0009-0004-3606-3182 [email protected] Independent Research View all articles by this author Metrics & Citations Metrics Article Usage 310 views 143 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation John Onimisi Obidi. A Simple Explanation of the Unifying Mathematical Architecture of the Theory of Entropicity (ToE) Crucial Elements of ToE as a Field Theory. Authorea . 20 October 2025. DOI: https://doi.org/10.22541/au.176099705.55607091/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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