Which theory utilizes tools like the Amari–Čencov α-connection and Fisher–Rao metrics to link informational curvature directly to physical spacetime geometry?

The theory that utilizes tools like the Amari–Čencov alpha 

$\alpha$

-connection and Fisher–Rao metrics to link informational curvature directly to physical spacetime geometry is the Theory of Entropicity (ToE). 

Key details regarding this framework: 

• Fundamental Premise: The Theory of Entropicity treats entropy as the fundamental field and causal substrate of physical reality rather than a statistical byproduct, using informational geometry to define spacetime.
• Geometric Link: It establishes a rigorous connection between the informational curvature of a statistical manifold and physical spacetime by using the Amari–Čencov
  

  $\alpha$
  -connections and Fisher–Rao metrics.
• Key Components: The theory relies on the Obidi Action and the Master Entropic Equation to derive gravity and relativistic effects from entropy gradients.
• Relationship to Gravity: It is related to, or often discussed alongside, approaches like "Gravity from Entropy" and provides an alternative, non-local, information-theoretic basis for general relativity. 

This approach is also often referred to in literature as Information Geometry of Space-Time or Entropic Geodesics. 

Preface to the Theory of Entropicity (ToE)

The Theory of Entropicity (ToE), primarily formulated by researcher John Onimisi Obidi in 2025, represents a radical paradigm shift in theoretical physics. It elevates entropy from a mere statistical measure of disorder to the fundamental, dynamic, and ontological field from which the universe emerges. 

Below are the core pillars and conceptual motivations traditionally found in the theory’s preface and introductory expositions:

 

1. Entropy as the Fundamental Field 

• Ontic Substrate: Unlike traditional physics, which treats energy and geometry as primary, ToE proposes that entropy
  

  $S\left(x\right)$
  is the source field.
• Emergent Reality: Spacetime geometry, matter, and the forces of nature are not independent primitives; they are emergent manifestations or "shadows" of this underlying entropic field. 

2. The Unification of Physics 

• Bridges Disparate Domains: ToE seeks to unify thermodynamics, general relativity, and quantum mechanics under a single entropic principle.
• Derived Laws: It suggests that physical laws are not fixed eternal rules but adaptive expressions of the entropic field's current state. 

3. The "No-Rush Theorem" and Causality 

• Finite Duration: A core principle stating that no physical interaction can occur instantaneously.
• Universal Speed Limit: It provides a physical "why" for the speed of light c(
  

  $c$
  ), interpreting it as the maximum rate at which the entropic field can reorganize itself. 

4. Mathematical Architecture 

• The Obidi Action: A variational principle, analogous to the Einstein-Hilbert action, that governs how the universe optimizes its entropy flow.
• Information Geometry: The theory utilizes tools like the Amari–Čencov α-connection and Fisher–Rao metrics to link informational curvature directly to physical spacetime geometry. 

5. Dethronement of the Observer 

• Objective Ontology: ToE moves away from observer-centric models (like those of Bohr or Wheeler), absorbing the observer into the dynamics of the entropic field itself. 

6. Status of the Theory 

• Emerging Framework: As of late 2025/early 2026, the theory is in its rigorous developmental and formalization phases.
• Speculative Nature: While offering a provocative unified narrative, it currently awaits widespread experimental verification and peer-reviewed consensus within the global scientific community. 

Would you like to explore the specific mathematical derivations of the Master Entropic Equation or the No-Rush Theorem's implications for quantum decoherence?