What is the Theory of Entropicity (ToE)? A Simple Expository Essay on a Radical and Audacious Theory in Modern Theoretical Physics 

The Theory of Entropicity (ToE), first formulated and further developed by John Onimisi Obidi, is a proposed unifying framework in which **entropy** and information are treated as the fundamental physical reality, with spacetime, matter, fields, and forces emerging from entropic and informational dynamics rather than existing as primary entities.[1][2][4][5][6]

## Core idea

In ToE, entropy is promoted from a statistical bookkeeping quantity to an active field $$S(x)$$ (or an entropic field $$\Phi_E(x^\mu)$$) whose gradients and flow drive all physical phenomena.[4][5][6] The visible universe is interpreted as a thermodynamic “projection” or image of an underlying informational manifold, where information and its entropic evolution generate what we experience as geometry, energy, and matter.[1][5][6]

## Entropy as the fundamental field

ToE postulates that all interactions, motion, and apparent curvature arise from the flow and redistribution of entropy, not from intrinsic forces or a fundamentally curved spacetime.[4][5]

- Objects do not intrinsically attract or repel; instead, they follow paths dictated by entropy gradients and maximization.[4]

- Spacetime does not fundamentally curve on its own; the appearance of curvature is produced by variations and curvature in the entropic field.[4][1]

- Forces are not independent entities but emergent descriptions of how systems evolve along entropy-driven optimal paths.[4][5]

An illustrative example is the reinterpretation of gravity: rather than being a fundamental force (Newton) or pure spacetime curvature (Einstein), gravity is treated as an emergent phenomenon arising from entropic constraints and gradients in the entropic field.[2][4]

## Key mathematical and conceptual structures

Several structural elements are highlighted in the Theory of Entropicity program:

- A bridging relation of the form $$\hbar c = k_B T_S \ell_S$$ links quantum $$\hbar$$, relativistic $$c$$, and thermodynamic $$k_B$$ constants via an “entropic temperature” and length scale, providing a bridge between information, energy, and curvature.[1]

- The Obidi Action is introduced as an informational/entropic action principle from which field equations are derived, analogous to how the Einstein–Hilbert action generates Einstein’s equations.[1][5]

- An Informational–Geometric Field Equation generalizes Einstein’s field equation into an informational-entropic context, treating geometry as emergent from informational curvature and entropy flow.[1][5]

- The framework uses information geometry (e.g., Čencov-type connections) to give a rigorous mathematical foundation to entropy-driven dynamics.[5][6]

These structures aim to unify thermodynamics, relativity, and quantum theory into one entropic/informational continuum.[1][5][6]

## Physical implications and examples

The ToE program has been applied to several phenomena to demonstrate its explanatory power:

- Mercury’s perihelion precession is re-derived using entropy-corrected Newtonian gravity (via an Entropic Force-Field Hypothesis), recovering the same 43 arcseconds per century that Einstein obtained, but attributing the effect to entropy constraints rather than spacetime curvature.[2][4]

- Relativistic effects such as mass increase, time dilation, and length contraction are reinterpreted as consequences of finite entropy propagation, entropic conservation, and redistribution—encoded in principles like the Entropic Resistance Principle, the Entropic Resistance Field, the Entropic Cone, and the No-Rush Theorem—rather than being postulated kinematically from spacetime geometry.[5][7]

- Phenomena like the Casimir effect, inertial mass, and gravity are framed as expressions of entropic curvature and informational temperature, without appealing to virtual particles or a pre-given quantum vacuum.[1][5]

A simple way to picture this is: instead of starting from spacetime and putting matter and fields in it, ToE starts from an underlying informational–entropic “substrate,” and shows how what we call spacetime, matter, and forces are efficient macroscopic encodings of how entropy flows and redistributes.[1][4][5][6]

## Philosophical position

Philosophically, the Theory of Entropicity treats information and entropy as ontologically primary, with the laws of physics emerging as constraints on self-organizing entropy flow in an informational continuum.[1][6] This places ToE in the broader family of informational and entropic approaches to fundamental physics, but it distinguishes itself by:

- Elevating entropy to a genuine field and causal substrate rather than a statistical descriptor.  

- Providing explicit entropic action principles and field equations intended to reproduce and generalize known gravitational and relativistic results.[1][2][4][5]

In our next exposition, we shall walk you through one concrete derivation (for example, the entropic derivation of Mercury’s perihelion shift or the entropic reinterpretation of the Lorentz factor) in more mathematical detail.

Citations:

[1] From the Temperature of Information to ... https://www.cambridge.org/engage/coe/article-details/69543375098cdc781fdccf9e

[2] The Theory of Entropicity (ToE): An Entropy-Driven ... https://www.cambridge.org/engage/coe/article-details/67e63abe6dde43c9086de9e0

[3] Entropy - Wikipedia https://en.wikipedia.org/wiki/Entropy

[4] The Theory of Entropicity (ToE): An Entropy-Driven https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/67e63abe6dde43c9086de9e0/original/the-theory-of-entropicity-to-e-an-entropy-driven-derivation-of-mercury-s-perihelion-precession-beyond-einstein-s-curved-spacetime-in-general-relativity-gr.pdf

[5] The Theory of Entropicity (ToE) Derives and Explains Mass ... https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/6900d89c113cc7cfff94ef3a/original/the-theory-of-entropicity-to-e-derives-and-explains-mass-increase-time-dilation-and-length-contraction-in-einstein-s-theory-of-relativity-to-r-to-e-applies-logical-entropic-concepts-and-principles-to-verify-einstein-s-relativity.pdf

[6] A Simple Explanation of the Unifying Mathematical ... https://www.authorea.com/users/896400/articles/1348176-a-simple-explanation-of-the-unifying-mathematical-architecture-of-the-theory-of-entropicity-toe-crucial-elements-of-toe-as-a-field-theory

[7] The Theory of Entropicity (ToE) Derives and Explains Mass ... https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5673430