On John Onimisi Obidi's Ingenious Application of Araki Relative Entropy in his Audacious and Radical Theory of Entropicity (ToE)

The "Theory of Entropicity" (ToE), first formulated and further developed by John Onimisi Obidi in early 2025, reframes entropy as a fundamental, dynamic field that generates spacetime, gravity, and quantum phenomena, with Araki Relative Entropy (a measure of difference between quantum states) playing a key role in defining its dynamics and constraints, moving beyond standard views where entropy is just statistical. ToE uses principles like the Spectral Obidi Action to derive physical laws, explaining relativity (time dilation, length contraction) and quantum effects as emergent consequences of entropic flow and finite-rate limits (like the speed of light) rather than fundamental kinematic rules, seeking a unified physics. 

Key Concepts in ToE

• Entropy as a Fundamental Field: Entropy isn't just disorder; it's the primary physical field, with its gradients creating curvature and motion.
• Araki Relative Entropy: Used as a dynamical action, not just a static measure, linking quantum states to the entropic field's behavior.
• Spectral Obidi Action: A variational principle governing the entropic field, generating dynamics and unifying physics.
• No-Rush Theorem: Sets finite limits on entropy redistribution, enforcing causality and the speed of light as entropic speed limits.
• Emergent Relativity: Time dilation and length contraction arise from entropic "capacity" constraints, not Minkowski geometry.
• Information Geometry: Integrates mathematical tools from information geometry (like Fisher-Rao metrics) to connect information flow with spacetime geometry. 

How ToE Uses Araki Relative Entropy

• In ToE, Araki Relative Entropy (a concept from quantum information theory) is a core mathematical tool to define the physical laws.
• It helps translate abstract quantum differences into concrete physical dynamics, connecting operators and geometry.
• It allows ToE to unify quantum mechanics (via spectral operators) and general relativity (via geometry) within a single entropic framework. 

In essence, ToE proposes that everything—space, time, gravity, quantum rules—emerges from the fundamental behavior and constraints of the entropic field, with Araki Relative Entropy providing crucial mathematical links. 

Further Explanatory Notes 

In 2026, the Theory of Entropicity (ToE), developed by John Onimisi Obidi, has gained attention for its radical treatment of entropy. Unlike standard physics, which views entropy as a statistical outcome, ToE promotes it to a fundamental dynamical field that generates the universe's geometry, matter, and laws. 

A cornerstone of this theory is its adaptation of Araki Relative Entropy, moving it from a static measurement tool into a core driver of physical evolution. 

Araki Relative Entropy in ToE 

Traditionally, Araki relative entropy is a rigorous mathematical measure used in quantum field theory to distinguish between two quantum states. In ToE, its role is transformed: 

• From Measure to Action: ToE integrates Araki relative entropy into the Spectral Obidi Action (SOA). Instead of just comparing states, the universe is modeled as seeking a path that extremizes an entropic functional based on Araki's formula.
• A Foundation for Dynamics: The "Spectral" aspect of the action relates to the spectrum of an entropy operator. The eigenvalues of this operator define the "heartbeat" of existence—limiting how fast the universe can rearrange information.
• Finite Measure: Because Araki relative entropy naturally cancels certain mathematical infinities (UV divergences) found in quantum field theory, it provides the "rigorous, finite" foundation ToE needs for its field equations. 

Core Architecture of the Theory of Entropicity (ToE) 

ToE aims to unify thermodynamics, relativity, and quantum mechanics through a single "entropic continuum". 

• Entropic Field (
  

  $S\left(x\right)$
  ): Entropy is the primary ontological substrate. Spacetime curvature, matter, and forces are merely secondary "localized configurations" or "vibrations" of this invisible informational field.
• Master Entropic Equation (MEE): Derived from the Obidi Action, this equation acts as the entropic equivalent of Einstein's field equations, governing how entropy gradients produce what we perceive as gravity.
• No-Rush Theorem: This principle reinterprets the speed of light (
  

  $c$
  ) as the maximum rate of entropic reorganization. It posits that information cannot rearrange itself instantaneously, thus giving rise to causality and relativistic effects like time dilation.
• Observer Dethroned: ToE argues that reality is computed by the entropic field prior to observation; perception is a downstream effect of entropic transitions rather than a primary cause. 

Comparisons with Other Theories

Feature	Traditional Physics	Theory of Entropicity (ToE)
Status of Entropy	Secondary/Emergent	Fundamental/Ontological
Space & Time	Pre-existing stage	Emergent from entropy flow
Araki Entropy	Diagnostic tool for states	Generator of dynamics (Action)
Gravity	Geometric curvature (GR)	Entropy gradient effect

ToE also claims to subsume other "entropic gravity" models, such as those by Ginestra Bianconi and Erik Verlinde, by showing their results are specific "linearized" or "boundary" cases of the broader entropic field theory. 

Would you like to explore the mathematical derivations of the Master Entropic Equation or see how ToE explains specific phenomena like dark energy?