The Mathematical Ingenuity, Sophistication and Complexity of the Theory of Entropicity (ToE)

The mathematical complexity of the Theory of Entropicity (ToE) stems from its ambition to unify physics by framing entropy as a fundamental field, which requires a sophisticated and unconventional mathematical framework that combines information geometry and non-equilibrium thermodynamics. Its complexity is characterized by the use of concepts like α-connections, non-extensive entropy formalisms (Rényi and Tsallis), and an iterative, self-correcting computational logic instead of classical differential geometry. This requires developing the Obidi Action and the Master Entropic Equation (MEE) to describe how entropy deforms and creates spacetime and gravity.

Key areas of mathematical complexity

Unifying diverse frameworks: ToE aims to provide a single framework that integrates the distinct mathematical languages of thermodynamics, general relativity, and quantum mechanics by treating entropy as the central, unifying element.

Information geometry and gravity: It builds upon concepts from information geometry, such as the Fisher-Rao metric, and transforms them into physical metrics of spacetime curvature. This involves using non-extensive formalisms (Rényi-Tsallis α-q) to mathematically link information flow to geometric structures.

Entropy as an ontological field:

Rather than a statistical byproduct, entropy is the fundamental field 𝑆(𝑥,𝑡) whose dynamics are governed by the Obidi Action and described by the Master Entropic Equation (MEE), which is the entropic analogue of Einstein's field equations.

Computational and iterative logic:

ToE’s mathematical model is described as more akin to computation and artificial intelligence than classical calculus because the field doesn't just evolve within spacetime; it evolves the geometry itself through an iterative process.

Formalization and new equations:

The theory requires the development of new equations, such as the Obidi Action and the Master Entropic Equation, and further formalization of concepts like the full quantization of the entropy field.

Ongoing development:

While a foundational structure exists, ToE is still in a state of active development, with ongoing efforts to provide more explicit and detailed mathematical constructions, especially concerning the full quantization of the entropy field and its coupling to standard model fields, as noted in critical reviews on various online publication repositories, such as OSF, Authorea, ResearchGate, SSRN, International Journal of Current Science Research and Review (IJCSRR), Cambridge University Open Engage (CoE).

Sources — help

References

Obidi, John Onimisi. (12th November, 2025). On the Theory of Entropicity (ToE) and Ginestra Bianconi’s Gravity from Entropy: A Rigorous Derivation of Bianconi’s Results from the Entropic Obidi Actions of the Theory of Entropicity (ToE). Cambridge University. https//doi.org/10.33774/coe-2025-g7ztq
John Onimisi Obidi. (6th November, 2025). Comparative analysis between john onimisi obidi’s theory of entropicity (toe) and waldemar marek feldt’s feldt–higgs universal bridge (f–hub) theory. International Journal of Current Science Research and Review, 8(11), pp. 5642–5657, 19th November 2025. URL:https: //doi.org/10.47191/ijcsrr/V8-i11–21.
Obidi, John Onimisi. 2025. On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics. Cambridge University. Published October 17, 2025. https://doi.org/10.33774/coe-2025-1dsrv
Obidi, John Onimisi (17th October 2025). On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics. Figshare. https://doi.org/10.6084/m9.figshare.30337396.v2
Obidi, John Onimisi. 2025. A Simple Explanation of the Unifying Mathematical Architecture of the Theory of Entropicity (ToE): Crucial Elements of ToE as a Field Theory. Cambridge University. Published October 20, 2025. https://doi.org/10.33774/coe-2025-bpvf3
Obidi, John Onimisi (15 November 2025). The Theory of Entropicity (ToE) Goes Beyond Holographic Pseudo-Entropy: From Boundary Diagnostics to a Universal Entropic Field Theory. Figshare. https://doi.org/10.6084/m9.figshare.30627200.v1
Obidi, John Onimisi. Unified Field Architecture of Theory of Entropicity (ToE). Encyclopedia. Available online: https://encyclopedia.pub/entry/59276 (accessed on 19 November 2025).
Obidi, John Onimisi. (4 November, 2025). The Theory of Entropicity (ToE) Derives Einstein’s Relativistic Speed of Light © as a Function of the Entropic Field: ToE Applies Logical Entropic Concepts and Principles to Derive Einstein’s Second Postulate. Cambridge University. https://doi.org/10.33774/coe-2025-f5qw8-v2
Obidi, John Onimisi. (28 October, 2025). The Theory of Entropicity (ToE) Derives and Explains Mass Increase, Time Dilation and Length Contraction in Einstein’s Theory of Relativity (ToR): ToE Applies Logical Entropic Concepts and Principles to Verify Einstein’s Relativity. Cambridge University. https://doi.org/10.33774/coe-2025-6wrkm
HandWiki contributors, “Physics:Theory of Entropicity (ToE) Derives Einstein’s Special Relativity,” HandWiki, https://handwiki.org/wiki/index.php?title=Physics:Theory_of_Entropicity_(ToE)_Derives_Einstein’s_Special_Relativity&oldid=3845936

Further Resources on the Theory of Entropicity (ToE):

Theory of Entropicity (ToE) by John Onimisi Obidi

The Mathematical Ingenuity, Sophistication and Complexity of the Theory of Entropicity (ToE)