The Spectral Obidi Action and its Potent Unification in the Theory of Entropicity (ToE)

The "Theory of Entropicity (ToE)" is a proposed framework, by John Onimisi Obidi, that aims to unify physics by treating entropy as a fundamental, dynamical field rather than a passive measure. The theory uses the "Spectral Obidi Action" as its variational principle to derive field equations, which are then used to incorporate and extend concepts like Ginestra Bianconi's "Gravity from Entropy," entropic gravity, information geometry, and generalized thermodynamics. This approach seeks to provide a single coherent framework where spacetime geometry, motion, and interactions emerge from the dynamics of this entropic field. 

Core components of the theory

Obidi Action: A variational principle that serves as the foundational mathematical backbone of the theory. It is used to derive the theory's fundamental equations, the Master Entropic Equation (MEE).

Entropy as a field: ToE proposes that entropy is not just a measure of disorder, but a universal, dynamical field that generates all physical phenomena, including gravity, motion, and quantum uncertainty.

Information geometry: The theory integrates information theory through the use of Amari–Čencov α-connections and metrics like the Fisher–Rao metric, creating a framework where information flow and spacetime geometry are mathematically linked.

Generalized thermodynamics: ToE incorporates and expands upon concepts in thermodynamics, including the Araki relative entropy for quantum states, and reformulates it as a central component of the universe's dynamics.

Entropic geodesics: The theory introduces "entropic geodesics" and an Entropy Potential Equation to describe the motion of systems within the entropic field, replacing the traditional geodesics of general relativity.

Causality: Causality is framed as a consequence of the finite rate at which entropy can be redistributed, formalized by the No-Rush Theorem, which is also proposed to be the origin of the constancy of the speed of light. 

Relation to other theories

Ginestra Bianconi's work: ToE is presented as a framework that naturally includes Bianconi's "Gravity from Entropy." Her results, such as the auxiliary G-field and a small positive cosmological constant, are presented as limiting cases within the broader entropic field dynamics of ToE.

Other entropic gravity models: ToE also encompasses other entropic gravity ideas, including those from Erik Verlinde (emergent gravity) and Ted Jacobson (horizon thermodynamics), by showing how they are specific instances of the more general entropic field.

Unification: The ultimate goal is to provide a single, unified framework for thermodynamics, quantum mechanics, and general relativity, by showing how they all emerge from the same fundamental entropic field.