The Entropic Cone of the Theory of Entropicity (ToE) Reframes Einstein's Light Cone of the Theory of Relativity (ToR)

 ## The Theory of Entropicity (ToE)

The **Theory of Entropicity (ToE)**, proposed and developed by **John Onimisi Obidi** starting in 2025, is a theoretical physics framework that redefines **entropy** not as a statistical measure of disorder, but as the **fundamental, dynamic field** from which all physical reality emerges.  According to ToE, entropy $S(x,t)$ is a continuous, causal substrate that generates motion, gravity, time, information flow, and the structure of spacetime itself. 

Rather than treating entropy as a byproduct of physical processes, ToE posits it as the **primary driver** of reality—unifying thermodynamics, general relativity, quantum mechanics, and information theory within a single entropic continuum.

### Core Principles of ToE

1. **Entropy as a Fundamental Field**  

   ToE elevates entropy to a real, dynamic field $S(x,t)$ that permeates spacetime. Gradients and variations in this field generate physical phenomena such as motion, inertia, and gravitation. This contrasts with general relativity, where gravity arises from spacetime curvature, and instead suggests that curvature itself emerges from entropic dynamics. 

2. **Obidi Action and the Master Entropic Equation (MEE)**  

   Central to ToE is the **Obidi Action**, a variational principle that governs the evolution of the entropy field.  From this action, the **Master Entropic Equation (MEE)** is derived, serving as the entropic analog of Einstein’s field equations:

   $$

   \text{MEE: } \mathcal{E}_{\mu\nu} = \kappa T_{\mu\nu}

   $$

   where $\mathcal{E}_{\mu\nu}$ represents entropic curvature and $T_{\mu\nu}$ is the energy-momentum tensor. 

3. **Entropic Origin of Relativity**  

   ToE derives relativistic effects—**time dilation, length contraction, and mass increase**—not from Lorentz symmetry or spacetime geometry, but from **entropic conservation laws** and the **Entropic Resistance Principle (ERP)**.  The finite speed of light $c$ is reinterpreted as the **maximum rate of entropic rearrangement**. 

   The **entropic Lorentz factor** emerges naturally:

   $$

   \gamma_{\text{ent}} = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}

   $$

   as a consequence of entropy redistribution between motion and timekeeping. 

4. **Entropic Time Limit (ETL)**  

   ToE introduces a **minimum irreducible time interval**—the **Entropic Time Limit (ETL)**—below which no physical interaction, measurement, or observation can occur.  This provides a causal foundation for quantum non-instantaneity, supported by attosecond-scale observations of entanglement formation (~232 attoseconds). 

5. **Entropic Geodesics and the Vuli–Ndlela Integral**  

   Particle trajectories are governed by **entropic geodesics**, derived from entropy gradients rather than metric curvature.  The **Vuli–Ndlela Integral** reformulates Feynman’s path integral with entropy weighting, introducing intrinsic irreversibility and temporal asymmetry into quantum mechanics:

   $$

   \mathcal{Z} = \int \mathcal{D}[x(t)] \, e^{-\eta \, \mathcal{S}_{\text{ent}}[x(t)]}

   $$

   where $\eta$ is the **entropic coupling constant** and $\mathcal{S}_{\text{ent}}$ is the entropic action. 

6. **Entropic Accounting Principle (EAP)**  

   ToE asserts that every physical process incurs an **Entropic Cost (EC)**.  The **Entropic Accounting Principle (EAP)** states that nature maintains an "entropy ledger," where no event—interaction, measurement, or observation—can occur without paying an equivalent entropic cost.

### Predictions and Validations

- **Gravitational Light Bending**: ToE reproduces Einstein’s prediction of **1.75 arcseconds** deflection of starlight by the Sun, without invoking spacetime curvature.  Instead, it uses an **entropic coupling constant $\eta$** and entropic geodesics. 

- **Mercury’s Perihelion Precession**: ToE derives the observed **43 arcseconds per century** precession using entropy-corrected Newtonian gravity, incorporating insights from the Unruh effect, Hawking temperature, and the holographic principle. 

- **Entropic Cones**: ToE replaces the relativistic **light cone** with **entropic cones**, defined by the inequality:

  $$

  G_{\alpha\mu\nu}(x) v^\mu v^\nu \leq 0

  $$

  which constrains causal directions based on the maximum rate of entropic reconfiguration.

### Unification and Implications

ToE unifies physics by showing that:

- General relativity emerges as a limiting case of entropic field dynamics.

- Quantum mechanics gains a thermodynamic foundation via the Vuli–Ndlela Integral.

- Thermodynamics is no longer emergent but **ontologically primary**. 

The framework also extends beyond physics into **cosmology, computation, AI, and philosophy**, suggesting that **consciousness and information processing** may arise as constraints of the entropic field.