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.