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Theory of Entropicity (ToE)

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What Is the Theory of Entropicity (ToE)?

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 framework provides 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 metrics are shown to transform into physical metric–affine geometries under entropy-driven deformation governed by the Rényi–Tsallis α–q formalism. Within this structure, entropy acts as an ontological scalar field S(x,t) — or more correctly, we write it in the generalized pre-geometric and pre-temporal form S(Λ) — 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 underlying space, time, and matter.

Ultimately, the Theory of Entropicity 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.

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.

A Brief Overview of the Theory of Entropicity (ToE)

Key Concepts, Impact, Implications, and Applications

The Theory of Entropicity (ToE) proposes that entropy is a fundamental field that drives physical processes, including gravity, challenging traditional views in physics.

Overview of the Theory

The Theory of Entropicity (ToE), primarily attributed to researcher John Onimisi Obidi, reinterprets physical phenomena through the lens of entropy. It posits that entropy is not merely a measure of disorder but a dynamic field that governs interactions and the evolution of systems across scales ranging from cosmology to quantum mechanics.

Key Concepts

1. Entropy as a Fundamental Field

ToE suggests that entropy acts as a physical field influencing the structure and behavior of matter and energy. This marks a departure from the traditional statistical interpretation of entropy.

2. Gravity as an Emergent Phenomenon

Gravity is not fundamental in this framework. Instead, it emerges from constraints imposed by the entropic field. Gravitational interactions arise from entropy-driven processes rather than spacetime curvature alone.

3. The No-Rush Theorem

A core principle of ToE: no physical interaction is instantaneous. All processes require finite time because entropy governs the pace of physical events.

4. Unification of Forces

ToE aims to unify all forces and fields under the dynamics of entropy, suggesting that all physical phenomena are manifestations of entropic processes.

5. Implications for Quantum Mechanics

Quantum phenomena such as entanglement and wave-function collapse are interpreted as processes constrained by the entropic field, not instantaneous events.

Potential Impact

The Theory of Entropicity has the potential to bridge gaps between classical physics and quantum mechanics, offering a new perspective on gravity and other fundamental forces. It challenges established theories and invites further exploration and experimental verification.

Foundational Principle

Proposed by John Onimisi Obidi in February 2025, ToE restructures our understanding of the universe by treating entropy as the primary field of existence, not a derived statistical quantity.

In traditional physics, entropy measures disorder emerging from microstates. In ToE, entropy is the dynamic fabric from which space, time, matter, motion, and information emerge.

Entropy Field E ⇒ Space, Time, Motion, Matter, Information

Entropic Manifold

ToE posits that the universe is an entropic manifold, a high-dimensional structure whose evolution is governed by gradient-driven ontodynamics: 

    dE/dt = − ∇ F(E)

Here, F(E) denotes an entropic potential capturing system interactions, and ∇ is the generalized entropy gradient. Traditional geometric notions such as curvature in General Relativity are replaced by entropy-driven flow of structure.

Active Medium and Field Dynamics

In ToE, space is not an inert background but an active medium activated by entropy. All physical processes — interactions, measurements, causal evolution — are modulated by the entropic field.

The speed of information propagation (related to the speed of light c) is reframed as the maximum rate at which entropy can be rearranged or transmitted: 

    c_entropy = max | dE/dt |

Physical laws, including gravitation and motion, emerge from local and global entropy dynamics rather than being imposed on pre-existing spacetime.

Implications and Applications

Conceptual Summary

Entropy is fundamental ⇒ All physical laws and constants are emergent.

This conceptual shift frames the universe as governed by entropy gradients rather than rigid geometric constraints, unifying physical phenomena under a single entropic paradigm.

References for Further Study

In essence, the Theory of Entropicity reconceptualizes reality as an entropy-first universe, with dynamic, information-rich fields driving structure, motion, and the observable phenomena of spacetime.

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 developed by John Onimisi Obidi, is a proposed unifying framework in which entropy and information are treated as the fundamental physical reality. In this view, spacetime, matter, fields, and forces emerge from entropic and informational dynamics rather than existing as primary entities.

Core Idea

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

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.

Gravity, for example, is treated not as a fundamental force or pure spacetime curvature, but as an emergent phenomenon arising from entropic constraints and gradients.

Key Mathematical and Conceptual Structures

These structures aim to unify thermodynamics, relativity, and quantum theory into a single entropic–informational continuum.

Physical Implications and Examples

Instead of starting from spacetime and placing matter and fields within it, ToE begins with an informational–entropic substrate and shows how spacetime, matter, and forces emerge as efficient macroscopic encodings of entropy flow.

Philosophical Position

Philosophically, ToE treats information and entropy as ontologically primary, with the laws of physics emerging as constraints on self-organizing entropy flow in an informational continuum.

ToE distinguishes itself by:

In the next exposition, we will walk through a concrete derivation — such as the entropic derivation of Mercury’s perihelion shift or the entropic reinterpretation of the Lorentz factor.

Citations

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