The Spectral Obidi Action (SOA) of the Theory of Entropicity (ToE)

The Spectral Obidi Action is a foundational mathematical construct within John Onimisi Obidi's proposed Theory of Entropicity (ToE), a framework that attempts to unify thermodynamics, relativity, and quantum mechanics by elevating entropy to a fundamental field of reality. 

The Spectral Obidi Action is described in the following ways:

Quantum Encoding: It introduces a Dirac-type entropy operator, the spectrum (the set of all possible eigenvalues) of which regulates properties like quantum coherence, scale, and regularity.

Duality to Local Action: It is a global formulation that complements the "Local Obidi Action," which describes the differential dynamics of the entropy field (related to classical geometry).

Operator Geometry: The action gives rise to an "operator geometry" derived from the asymptotics of its associated operator, directly linking spectral data to geometric structure.

Integration of Concepts: This spectral perspective allows ToE to encode quantum features, such as the Araki relative entropy (used for comparing quantum states), directly into the entropic field's mathematics, rather than adding them as external assumptions.

Variational Principle: Like the Einstein-Hilbert action in general relativity, the Spectral Obidi Action (along with the local action) is a variational principle from which the core "Master Entropic Equation" (MEE) — the governing equation of the entropy field — is derived. 

In essence, the Spectral Obidi Action (SOA) is the part of ToE's mathematical architecture that incorporates quantum mechanics by defining the fundamental field's properties through spectral analysis, ensuring coherence and irreversibility are intrinsic features of the entropic field. 

More information can be found in papers available on platforms such as Medium, SSRN, Authorea, International Journal of Current Science Research and Review (IJCSRR) Cambridge University Open Engage (CoE), etc.