How Did Obidi Use Tsallis Entropy in the Mathematical Development of the Theory of Entropicity (ToE)?

In John Onimisi Obidi’s Theory of Entropicity (ToE), first introduced in 2025, Tsallis entropy is used as a parameterization for deforming informational geometry into physical spacetime geometry. 

Within this framework, Obidi utilizes the Rényi-Tsallis

$\alpha$

-

$q$

formalism to establish a mathematical bridge between information flow and physical curvature through the following methods: 

• Geometric Deformation: Obidi uses Tsallis entropy to transform statistical metrics—such as the Fisher-Rao (classical) and Fubini-Study (quantum) metrics—into physical metric-affine geometries.
• The Constitutive Relation: He introduces the mathematical link
  

  $\alpha =2(1-q)$
  , where
  

  $q$
  (the Tsallis non-extensivity parameter) is tied to
  

  $\alpha$
  (the Amari-Čencov affine connection). This relation maps non-extensive entropy deformation to affine asymmetry in spacetime.
• Ontological Scalar Field: Tsallis entropy is integrated into the Obidi Action, a variational principle where entropy is treated as an ontological scalar field
  

  $S(x,t)$
  . This results in the Master Entropic Equation (MEE), which describes how informational curvature becomes physical gravity and motion.
• Unification of Scales: By incorporating Tsallis entropy, the theory absorbs non-extensive statistical mechanics as a special case of a broader entropic manifold, allowing it to describe both local differential dynamics and global spectral constraints. 

Detailed expositions on these mathematical foundations can be found in Obidi's research on TechRxiv and the Encyclopedia of World Problems and Human Potential.