The Theory of Entropicity (ToE) as a comprehensive Framework for the Unification of Physics from a Single Principle of Entropy 

The Theory of Entropicity (ToE) is a comprehensive framework developed by John Onimisi Obidi that redefines entropy as the fundamental physical field underlying all natural phenomena — the ultimate causal substrate of the universe.

1. Core Idea

Unlike classical thermodynamics, where entropy is treated as a statistical measure of disorder, the Theory of Entropicity posits that entropy is a real, dynamic field — an entity that drives motion, gravitation, time, and information flow.

In ToE, the universe evolves not because of forces or geometric curvature but because entropy continuously redistributes itself to minimize constraints and maximize flow. This entropy flow generates what we perceive as physical laws, motion, and even the structure of spacetime.

2. The Obidi Actions: Local Obidi Action (LOA) and Spectral Obidi Action (SOA)

At the heart of the Theory of Entropicity (ToE) lies the Obidi Action, a variational principle analogous to the Einstein–Hilbert action in General Relativity (GR).

It formulates the dynamics of the entropic field and unifies thermodynamics, quantum mechanics, and relativity.

From it arise:

1. The Master Entropic Equation (MEE)Entropic Geodesics, which describe motion as entropy minimization paths
2. The Entropy Potential Equation, governing field interactions

3. Mathematical Foundations

ToE integrates multiple information geometries and entropy measures into one unified mathematical system:

1. Fisher–Rao and Fubini–Study metrics for statistical and quantum geometries
2. Amari–Čencov α-connections for generalized curvature in entropy space
3. Relative entropy (Kullback–Leibler, Rényi, Tsallis, and Araki) for dynamic field measures

This gives entropy its own geometry and kinematics, producing a manifold where the curvature represents entropy gradients.

4. Key Concepts

1. Entropy Field (S(x)): The scalar–tensor field that governs physical evolution.
2. Vuli-Ndlela Integral: A reformulation of Feynman’s Path Integral enforcing irreversible, entropy-driven constraints.
3. Entropic Time Limit (ETL): The smallest possible time for any interaction — more fundamental than Planck time.
4. Entropic Geodesics: The “least-constraint” paths followed by all systems in the entropy field.
5. Entropic Observability and Existentiality: Frameworks defining when a system can exist or be observed based on entropy thresholds.

5. Physical Implications

1. Gravity emerges from entropy curvature, not from spacetime curvature.
2. Time dilation and length contraction result from entropy redistribution, not from relative motion per se.
3. Quantum entanglement is an entropy synchronization process — the exchange of entropic information.
4. Mass arises from internal entropy content — matter is “condensed entropy.”

6. Empirical Outlook

The Theory of Entropicity (ToE) interprets attosecond entanglement formation experiments as direct evidence of entropy’s physical dynamics.

It predicts measurable quantities such as entropy lensing, entropic curvature corrections, and time-asymmetric (irreversible) quantum effects.

In essence, the Theory of Entropicity aims to unify physics from a single principle — Entropy — showing that:

“Energy is entropy in motion, gravity is entropy’s curvature, and quantum probability is entropy’s irreversibility.”