Both Information and Geometry Have Temperatures Associated with Them According to the Theory of Entropicity (ToE)

The theory that explicitly posits that information and geometry have an intrinsic temperature (often referred to as "informational temperature" or "temperature of geometry") is the Theory of Entropicity (ToE), as formulated and developed by John Onimisi Obidi. 

Key Concepts of the Theory of Entropicity (ToE): 

• Definition: ToE proposes that entropy and information form the fundamental foundation of physical reality, with spacetime, matter, and gravitation emerging as thermodynamic projections of an invisible informational manifold.
• Temperature of Information: Instead of traditional kinetic energy, temperature in ToE is defined as the rate of informational change (or intensity of entropy flow).
• Temperature of Geometry: Because geometry in ToE is generated by the informational field, this temperature extends to the geometry of spacetime itself. High informational activity corresponds to "hot geometry" (strong curvature), while low activity corresponds to "cold geometry" (weak curvature).
• Unification Relation: ToE introduces the fundamental relation
  

  $\hslash c=k_{B}T{\ell }_S$
  , which bridges quantum action (
  

  $\hslash$
  ), thermodynamic temperature (
  

  $T$
  ), and the geometric correlation length (
  

  ${\ell }_S$
  ).
• Reinterpretation of Physics: Phenomena such as gravity, inertia, and the Casimir effect are reinterpreted as consequences of entropic curvature and informational temperature. 

While other theories like Entropic Gravity (Verlinde) or the Holographic Principle (Bekenstein, Hawking) suggest that gravity and spacetime are thermodynamic in nature, the Theory of Entropicity (ToE) specifically introduces the concept of an intrinsic, non-zero temperature for the informational and geometric structure itself.