Obidi's Equations and Their Formulations and Implications in the Theory of Entropicity (ToE)

"Obidi's equations" refer to the core mathematical framework of John Onimisi Obidi's Theory of Entropicity (ToE), centered around the Obidi Action and the derived Master Entropic Equation (MEE), which treats entropy as a fundamental, dynamic field generating reality, motion, gravity, time, and information, unifying thermodynamics, relativity, and quantum mechanics through information geometry. Key components include the MEE (analogous to Einstein's field equations), Entropic Geodesics (describing paths), Entropy Potential Equation, and the No-Rush Theorem, all based on principles from information geometry like Fisher-Rao and Fubini-Study metrics. 

Key Equations & Concepts:

• Obidi Action: A variational principle defining the dynamics of the fundamental entropy field.
• Master Entropic Equation (MEE): The central field equation, governing how the entropy field evolves and creates physical phenomena, derived from the Obidi Action.
• Entropic Geodesics: Paths systems follow in the entropic manifold, driven by entropy gradients, not just spacetime curvature.
• Entropy Potential Equation: Describes how entropic forces manifest.
• No-Rush Theorem: States that new physical states can only emerge once their entropic curvature reaches a certain distinguishable threshold (ln 2), meaning reality can't "rush" beyond its entropic readiness.
• Information Geometry: Integrates metrics (like Fisher-Rao) to provide a rigorous framework, treating temperature as the rate of information/entropy reorganization and the speed of light as the maximum entropic rearrangement rate. 

Core Idea:

In ToE, entropy isn't just disorder; it's the fundamental stuff of reality, a dynamic field whose gradients create spacetime, gravity, time, and quantum behaviors, unifying physics under an information-theoretic lens. 

Appendix: Extra Matter

In the context of the

Theory of Entropicity (ToE) proposed by John Onimisi Obidi, "Obidi's equations" refer to a set of fundamental mathematical constructs that elevate entropy from a statistical property to a dynamic physical field. 

As of 2026, the core equations and constructs in this framework include: 

1. The Obidi Action 

The Obidi Action is the primary variational principle of the theory, serving a role similar to the Einstein-Hilbert action in General Relativity. It integrates geometric curvature, entropy gradients, and spectral information into a single principle that the universe is said to "optimize" as it evolves. 

2. The Master Entropic Equation (MEE) 

Often called the Obidi Field Equation (OFE), the MEE is the central dynamical law derived from the Obidi Action. 

• Purpose: It governs the evolution of the entropy field (
  

  $S(x,t)$
  ) in spacetime.
• Nature: It is nonlinear and nonlocal, typically requiring iterative computational methods rather than closed-form algebraic solutions.
• Analogy: It is viewed as the entropic analogue of Einstein's field equations, describing how entropy deforms and creates spacetime geometry. 

3. Entropic Geodesics 

These equations replace the standard geodesics of curved spacetime. They describe the natural trajectories of systems as being driven by entropy gradients rather than purely by the curvature of a pre-existing manifold. 

4. Entropy Potential Equation 

This equation defines the "energy landscape" of the entropy field. It provides the structural constraints for the MEE, guiding how entropic forces manifest and shape physical interactions. 

5. Supplemental Constructs 

• Vuli–Ndlela Integral: An entropy-weighted version of Feynman’s path integral that embeds the arrow of time and irreversibility directly into quantum mechanics.
• Entropy Flow Equation: A continuity equation governing the propagation of the scalar entropy field, often expressed through an entropic current (
  

  $J^m=\eta {𝜕}^{m}S$
  ).
• No-Rush Theorem: A mathematical proof within ToE asserting that entropy cannot redistribute instantaneously, which derives the speed of light (
  

  $c$
  ) as a consequence of this finite rate.