View source for Physics:The Theory of Entropicity(ToE) and Competing Theories in Physics

== Theory of Entropicity(ToE) and Competing Theories in Modern Theoretical Physics ==

The '''[[Theory of Entropicity(ToE)]]''', first formulated and developed by '''[[Biography:John Onimisi Obidi|John Onimisi Obidi]]''', <ref>Physics:Einstein's Relativity from Obidi's Theory of Entropicity(ToE). (2025, August 30). HandWiki, . Retrieved 12:19, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Einstein%27s_Relativity_from_Obidi%27s_Theory_of_Entropicity(ToE)&oldid=3742784</ref><ref>Physics:Time Dilation, Length Contraction in the Theory of Entropicity (ToE). (2025, August 30). HandWiki, . Retrieved 10:01, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Time_Dilation,_Length_Contraction_in_the_Theory_of_Entropicity_(ToE)&oldid=3742771</ref><ref>Physics:Insights from the No-Rush Theorem in the Theory of Entropicity(ToE). (2025, August 1). HandWiki, . Retrieved 09:43, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Insights_from_the_No-Rush_Theorem_in_the_Theory_of_Entropicity(ToE)&oldid=3741840</ref><ref>Physics:The Cumulative Delay Principle(CDP) of the Theory of Entropicity(ToE). (2025, August 11). HandWiki, . Retrieved 09:40, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:The_Cumulative_Delay_Principle(CDP)_of_the_Theory_of_Entropicity(ToE)&oldid=3742101</ref><ref>Physics:Theory of Entropicity(ToE), Time Quantization and the Laws of Nature. (2025, August 1). HandWiki, . Retrieved 09:34, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Theory_of_Entropicity(ToE),_Time_Quantization_and_the_Laws_of_Nature&oldid=3741802</ref><ref>Book:Conceptual and Mathematical Treatise on Theory of Entropicity(ToE). (2025, August 30). HandWiki, . Retrieved 09:31, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Book:Conceptual_and_Mathematical_Treatise_on_Theory_of_Entropicity(ToE)&oldid=3742769</ref><ref>Physics:Gravity from Newton and Einstein in the Theory of Entropicity(ToE). (2025, August 7). HandWiki, . Retrieved 09:19, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Gravity_from_Newton_and_Einstein_in_the_Theory_of_Entropicity(ToE)&oldid=3742006</ref><ref>Physics:Randomness and Determinism Unified in the Theory of Entropicity(ToE). (2025, August 13). HandWiki, . Retrieved 09:17, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Randomness_and_Determinism_Unified_in_the_Theory_of_Entropicity(ToE)&oldid=3742233</ref><ref>Physics:Relativity from Fundamental Postulate of Theory of Entropicity(ToE). (2025, August 30). HandWiki, . Retrieved 09:13, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Relativity_from_Fundamental_Postulate_of_Theory_of_Entropicity(ToE)&oldid=3742766</ref><ref>Physics:Artificial Intelligence Formulated by the Theory of Entropicity(ToE). (2025, August 27). HandWiki, . Retrieved 03:59, August 27, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Artificial_Intelligence_Formulated_by_the_Theory_of_Entropicity(ToE)&oldid=3742591</ref><ref>Physics:Curved Spacetime Derived from Obidi's Theory of Entropicity(ToE). (2025, August 29). HandWiki, . Retrieved 09:01, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Curved_Spacetime_Derived_from_Obidi%27s_Theory_of_Entropicity(ToE)&oldid=3742730</ref><ref>Physics:Information and Energy Redistribution in Theory of Entropicity(ToE). (2025, August 30). HandWiki, . Retrieved 09:05, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Information_and_Energy_Redistribution_in_Theory_of_Entropicity(ToE)&oldid=3742765</ref><ref>Obidi, John Onimisi (2025). Master Equation of the Theory of Entropicity (ToE). Encyclopedia. https://encyclopedia.pub/entry/58596</ref><ref name="obidi2025shapiro">Obidi, John Onimisi. ''Corrections to the Classical Shapiro Time Delay in General Relativity (GR) from the Entropic Force-Field Hypothesis (EFFH)''. Cambridge University. (11 March 2025). https://doi.org/10.33774/coe-2025-v7m6c</ref><ref name="obidi2025geee">Obidi, John Onimisi. ''How the Generalized Entropic Expansion Equation (GEEE) Describes the Deceleration and Acceleration of the Universe in the Absence of Dark Energy''. Cambridge University. (12 March 2025). https://doi.org/10.33774/coe-2025-6d843</ref><ref name="obidi2025perih">Obidi, John Onimisi. ''The Theory of Entropicity (ToE): An Entropy-Driven Derivation of Mercury’s Perihelion Precession Beyond Einstein’s Curved Spacetime in General Relativity (GR)''. Cambridge University. (16 March 2025). https://doi.org/10.33774/coe-2025-g55m9</ref><ref name="obidi2025starlight">Obidi, John Onimisi. ''The Theory of Entropicity (ToE) Validates Einstein’s General Relativity (GR) Prediction for Solar Starlight Deflection via an Entropic Coupling Constant η''. Cambridge University. (23 March 2025). https://doi.org/10.33774/coe-2025-1cs81</ref><ref>Obidi, John Onimisi (25 March 2025). "Attosecond Constraints on Quantum Entanglement Formation as Empirical Evidence for the Theory of Entropicity (ToE)". Cambridge University. https://doi.org/10.33774/coe-2025-30swc</ref><ref name="obidi2025reconcile">Obidi, John Onimisi. ''Einstein and Bohr Finally Reconciled on Quantum Theory: The Theory of Entropicity (ToE) as the Unifying Resolution to the Problem of Quantum Measurement and Wave Function Collapse''. Cambridge University.  (14 April 2025). https://doi.org/10.33774/coe-2025-vrfrx</ref><ref>Obidi, John Onimisi . "On the Discovery of New Laws of Conservation and Uncertainty, Probability and CPT-Theorem Symmetry-Breaking in the Standard Model of Particle Physics: More Revolutionary Insights from the Theory of Entropicity (ToE)". Cambridge University. (14 June 2025). https://doi.org/10.33774/coe-2025-n4n45</ref><ref name="obidi_addendum">Obidi, John Onimisi. ''A Critical Review of the Theory of Entropicity (ToE) on Original Contributions, Conceptual Innovations, and Pathways towards Enhanced Mathematical Rigor: An Addendum to the Discovery of New Laws of Conservation and Uncertainty''. Cambridge University.(2025-06-30). https://doi.org/10.33774/coe-2025-hmk6n</ref>
<ref>Physics:HandWiki Master Index of Source Papers on Theory of Entropicity(ToE). (2025, September 9). HandWiki, . Retrieved 17:33, September 9, 2025 from https://handwiki.org/wiki/index.php?title=Physics:HandWiki_Master_Index_of_Source_Papers_on_Theory_of_Entropicity(ToE)&oldid=3743060</ref><ref>Philosophy:Obidi's Agile Manifesto in Publishing of Revolutionary Ideas. (2025, September 9). HandWiki, . Retrieved 17:37, September 9, 2025 from https://handwiki.org/wiki/index.php?title=Philosophy:Obidi%27s_Agile_Manifesto_in_Publishing_of_Revolutionary_Ideas&oldid=3743065</ref><ref>Physics:Entrodynamic Bellman Equation of AI RL in Theory of Entropicity(ToE). (2025, September 10). HandWiki, . Retrieved 14:46, September 10, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Entrodynamic_Bellman_Equation_of_AI_RL_in_Theory_of_Entropicity(ToE)&oldid=3743125</ref><ref>Why language models hallucinate | OpenAI. (September 2025). https://openai.com/index/why-language-models-hallucinate/</ref><ref>Physics:On the Phenomenological Foundations of the Theory of Entropicity(ToE). (2025, September 15). HandWiki, . Retrieved 05:06, September 15, 2025 from https://handwiki.org/wiki/index.php?title=Physics:On_the_Phenomenological_Foundations_of_the_Theory_of_Entropicity(ToE)&oldid=3743204</ref><ref>Wikipedia contributors. (2025, May 7). Entropic uncertainty. In Wikipedia, The Free Encyclopedia. Retrieved 00:34, September 20, 2025, from https://en.wikipedia.org/w/index.php?title=Entropic_uncertainty&oldid=1289229404</ref><ref>Pawłowski, M. (2020). Entropy in Foundations of Quantum Physics. Entropy, 22(3), 371 https://doi.org/10.3390/e22030371</ref><ref>Physics:Entropy as Foundation of Quantum Mechanics in Theory of Entropicity. (2025, September 20). HandWiki, . Retrieved 01:29, September 20, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Entropy_as_Foundation_of_Quantum_Mechanics_in_Theory_of_Entropicity&oldid=3743315</ref><ref>Physics:The Theory of Entropicity (ToE) as a New Foundation for Cybersecurity. (2025, September 20). HandWiki, . Retrieved 02:29, September 20, 2025 from https://handwiki.org/wiki/index.php?title=Physics:The_Theory_of_Entropicity_(ToE)_as_a_New_Foundation_for_Cybersecurity&oldid=3743326</ref><ref>Physics:A Brief Introduction to the Theory of Entropicity(ToE) for Research. (2025, September 20). HandWiki, . Retrieved 08:55, September 20, 2025 from https://handwiki.org/wiki/index.php?title=Physics:A_Brief_Introduction_to_the_Theory_of_Entropicity(ToE)_for_Research&oldid=3743334</ref> is a proposed framework in theoretical physics that elevates [[Entropy]] from a statistical descriptor of disorder to a universal, local, dynamical scalar field. In this formulation, entropy is not merely a bookkeeping device for thermodynamic states or information-theoretic measures, but rather a fundamental field whose kinetics underlie all observations, measurements, and interactions.

So far, no mainstream theory has advanced this precise claim in full generality. While several traditions in physics and information theory elevate entropy or information to a foundational role, they typically do not postulate entropy as a standalone scalar field with its own field equations.

This paper, therefore, surveys the nearest families of theories that intersect with the ToE, highlighting both their convergences and divergences.

== Thermodynamic Origin of Gravity (Jacobson, 1995) ==

In 1995, Ted Jacobson derived Einstein’s field equations from the Clausius relation applied to local Rindler horizons.<ref name="Jacobson1995">Jacobson, T. (1995). “Thermodynamics of Spacetime: The Einstein Equation of State”. ''Physical Review Letters'' 75(7): 1260–1263.</ref> In this view, gravity emerges as an equation of state, with spacetime thermodynamics providing the underlying structure.

'''Similarity to ToE:''' Entropy is central, appearing in the thermodynamic derivation of spacetime dynamics.

'''Difference:''' Jacobson’s approach does not introduce a propagating entropy field; entropy remains a state function tied to horizons, not a universal scalar field permeating all interactions.


== Emergent Gravity and Horizon Thermodynamics (Padmanabhan) ==

T. Padmanabhan has developed a program where spacetime dynamics are tied to horizon entropy and the concept of “atoms of spacetime.”<ref name="Padmanabhan2010">Padmanabhan, T. (2010). “Thermodynamical Aspects of Gravity: New Insights”. ''Reports on Progress in Physics'' 73(4): 046901.</ref> Equipartition principles are used to derive gravitational field equations.

'''Similarity:''' Entropy is treated as a fundamental organizing principle of spacetime.

'''Difference:''' Entropy is not formulated as a dynamical scalar field; rather, it is a property of horizons and microscopic degrees of freedom.


== Entropic Gravity (Verlinde) ==

Erik Verlinde’s [[Entropic gravity]] (2010, 2016) proposes that gravity is an emergent entropic force arising from changes in information associated with the positions of material bodies.<ref name="Verlinde2010">Verlinde, E. (2010). “On the Origin of Gravity and the Laws of Newton”. arXiv:1001.0785.</ref> Verlinde later extended this to explain galactic rotation curves without invoking dark matter, attributing the effect to de Sitter entropy and entanglement.

'''Similarity:''' Comes closest to a field-like influence of entropy, with entropy gradients producing effective forces.

'''Difference:''' Entropy is framed as an emergent potential, not as a universal scalar field with intrinsic dynamics.


== Spacetime from Entanglement (Van Raamsdonk et al.) ==

Mark Van Raamsdonk and others have argued that spacetime geometry itself emerges from the entanglement structure of quantum states.<ref name="VanRaamsdonk2010">Van Raamsdonk, M. (2010). “Building up Spacetime with Quantum Entanglement”. ''General Relativity and Gravitation'' 42: 2323–2329.</ref> This perspective is deeply tied to the AdS/CFT correspondence and the Ryu–Takayanagi formula for entanglement entropy.

'''Similarity:''' Entropy and information are treated as structural foundations of geometry.

'''Difference:''' The focus is on information-theoretic structure, not a dynamical entropy field.


== Thermal Time Hypothesis (Connes & Rovelli) ==

The [[Thermal time hypothesis]] (1994) by Alain Connes and Carlo Rovelli proposes that the flow of time is determined by the thermodynamic state of a system, specifically through modular flow in operator algebras.<ref name="ConnesRovelli1994">Connes, A. & Rovelli, C. (1994). “Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in Generally Covariant Quantum Theories”. ''Classical and Quantum Gravity'' 11(12): 2899.</ref>

'''Similarity:''' Time itself is linked to thermodynamic/entropic considerations.

'''Difference:''' No field dynamics are introduced; entropy defines temporal flow, not a universal scalar field sourcing interactions.


== Entropic Dynamics (Caticha) ==

Ariel Caticha’s [[Entropic dynamics]] derives quantum theory from principles of entropic inference.<ref name="Caticha2012">Caticha, A. (2012). “Entropic Dynamics”. In: ''Bayesian Inference and Maximum Entropy Methods in Science and Engineering''. AIP Conf. Proc. 1443: 60–68.</ref> In this framework, entropy governs the updating of probability distributions, leading to the Schrödinger equation as an emergent law.

'''Similarity:''' Entropy is the driver of dynamics.

'''Difference:''' The dynamics are epistemic (probability updates), not ontological (a physical scalar field).


== Generalized Entropies and Nonequilibrium Order (Tsallis; England) ==

Constantino Tsallis introduced non-extensive entropy (Tsallis entropy), extending thermodynamics to complex systems.<ref name="Tsallis1988">Tsallis, C. (1988). “Possible Generalization of Boltzmann–Gibbs Statistics”. ''Journal of Statistical Physics'' 52(1–2): 479–487.</ref>

Jeremy England proposed that dissipative adaptation in far-from-equilibrium systems can be understood through entropy production.<ref name="England2013">England, J. (2013). “Statistical Physics of Self-Replication”. ''The Journal of Chemical Physics'' 139(12): 121923.</ref>

'''Similarity:''' Entropy is treated as foundational in complex systems and adaptation.

'''Difference:''' These approaches remain within statistical mechanics and biology, not fundamental field theory.


== Comparative Summary Table ==

{| class="wikitable" style="width:100%; text-align:center;"
|-
! Theory / Program 
! Role of Entropy 
! Field-like? 
! Domain of Application
|-
| Jacobson (1995) 
| Derives Einstein equations from Clausius relation 
| No 
| Gravity as thermodynamics
|-
| Padmanabhan 
| Horizon entropy, atoms of spacetime 
| No 
| Emergent spacetime
|-
| Verlinde 
| Entropic force, MOND-like effects 
| Partially 
| Gravity, dark matter alternatives
|-
| Van Raamsdonk 
| Geometry from entanglement entropy 
| No 
| Quantum gravity, AdS/CFT
|-
| Connes & Rovelli 
| Time from thermodynamic state 
| No 
| Foundations of time
|-
| Caticha 
| Entropic inference → quantum theory 
| No 
| Quantum foundations
|-
| Tsallis; England 
| Generalized entropy, adaptation 
| No 
| Complex systems, biology
|-
| '''Theory of Entropicity (ToE)''' 
| Entropy as universal dynamical scalar field 
| '''Yes''' 
| All interactions, measurements, observations, unification
|}

== Conclusion ==

Across physics, information theory, and complex systems science, entropy and information have been repeatedly elevated to foundational roles. However, these programs typically:

focus on a specific domain (gravity, time, quantum theory, or complex systems);

treat entropy as a state function, inference tool, or emergent property, not as a universal dynamical scalar field.


The '''Theory of Entropicity (ToE)''' distinguishes itself by proposing that entropy is a real, physical field with its own kinetics, capable of unifying all interactions and measurements. In this sense, ToE both converses with and diverges from existing traditions, positioning itself as a candidate unifying framework that extends beyond the scope of current entropic or informational approaches.

== See also ==

[[Entropic gravity]]

[[Emergent spacetime]]

[[Thermal time hypothesis]]

[[Quantum entanglement and spacetime]]

[[Non-extensive entropy]]


== References ==

{{Sourceattribution|The Theory of Entropicity(ToE) and Competing Theories in Physics|1}}