On the Significance of the Local Obidi Action (LOA) of the Theory of Entropicity (ToE) in Modern Theoretical Physics 

The Local Obidi Action (LOA) is a foundational component of the Theory of Entropicity (ToE), a theoretical physics framework developed by John Onimisi Obidi. It serves as a variational principle that redefines entropy not as a statistical byproduct of disorder, but as the primary, fundamental field from which spacetime, geometry, and physical laws emerge. 

The significance of the Local Obidi Action lies in its ability to unify disparate physical theories by making entropy the driving force of reality: 

• Unification of Physics: The LOA integrates thermodynamics, general relativity, and quantum mechanics into a single, cohesive framework.
• Geometric Coupling: It dictates how entropic gradients interact with the geometry of space itself, showing that spacetime curvature and gravity are manifestations of entropic flow, rather than independent, pre-existing structures.
• Derivation of Field Equations: The LOA generates the Master Entropic Equation (MEE), which is a nonlinear, generally covariant field equation that governs the evolution of the entropy field (
  

  $S\left(x\right)$
  ) and acts as an entropic counterpart to Einstein’s field equations.
• Irreversible Dynamics: Unlike standard, time-symmetric physical laws, the Local Obidi Action explicitly includes both reversible and irreversible processes, embedding the arrow of time directly into the fundamental dynamics of the universe.
• Emergent Phenomena: It explains phenomena such as inertial mass, gravity, and the Casimir effect as direct consequences of entropic curvature and capacity constraints.
• Non-local and Local Synergy: The LOA operates alongside the Spectral Obidi Action (SOA). While the LOA describes the differential (local) dynamics of the entropy field in spacetime, the SOA encapsulates global constraints. Together, they form a "dual structure" that ensures local interactions are consistent with global geometry. 

In essence, the Local Obidi Action shifts the foundational understanding of the universe from a "geometric" perspective (Einstein) to an "entropic" perspective, where entropy generates the geometry. 

Scholium/Remarks on the Dual Structure of the Obidi Action on Local Interactions and Global Constraints 

In the Theory of Entropicity (ToE) proposed by John Onimisi Obidi, the "dual structure" formed by the Spectral Obidi Action (SOA) and the Local Obidi Action (LOA) ensures that microscopic, day-to-day physical events (local interactions) remain consistent with the overall shape and structure of the universe (global geometry). 

Here is a breakdown of what this means:

1. The Components of the "Dual Structure"

• LOA (Local Obidi Action): This represents the dynamics of the entropic field on a small scale, governing how matter moves and interacts in specific, local locations. It is responsible for the "no-rush" principle, meaning local actions take finite time to occur.
• SOA (Spectral Obidi Action): This represents the global or "operator" geometry, treating physical reality as a spectral (vibrational/informational) structure rather than just a physical one. It connects local events to the overall curvature of the entropic field. 

2. "Local Interactions" Consistent with "Global Geometry"

The core claim is that entropy, not spacetime, is fundamental. 

• Local Interactions: The movements of particles, quantum measurements, and individual physical interactions.
• Global Geometry: The large-scale structure of the universe (curvature, expansion, etc.), which in ToE is emergent, not fundamental. 

Together, the SOA and LOA bridge the gap between microscopic events and macroscopic spacetime, ensuring that as entropy increases locally (local interaction), it also shapes the overall curvature of the universe (global geometry) consistently. 

3. Key Implications of this Duality

• Entropy-Driven Geometry: Rather than gravity creating curvature (as in General Relativity), the local and global actions of the entropic field create the geometry.
• Consistency: The dual structure prevents contradictions between what happens locally (e.g., quantum measurements) and what is observed globally (e.g., gravity), as both are governed by the same underlying entropic field.
• Unified Framework: By linking spectral operator actions (SOA) and local actions (LOA), the theory bridges the gap between quantum mechanics (often dealing with the local/probabilistic) and general relativity (global geometry). 

1.  What the Obidi Action idea captures:

Obidi’s Local Obidi Action (LOA) plays the role of a local field theory: it describes how the entropic field S(x) changes in small regions—essentially, the dynamics one could in principle measure in laboratories or in quantum systems.

The Spectral Obidi Action (SOA) extends that description to the global or spectral domain: rather than integrating over points in space, it acts over the spectrum of geometric operators (curvature, Laplacians, or information-geometry eigenmodes).  It encodes the “shape” or information content of the entire universe.

Putting them together, the position of ToE is that the same entropic quantity that drives small-scale interactions also determines the large-scale curvature of the universe.  It’s an attempt to create a bridge between quantum dynamics and cosmological geometry.

2.  How this compares with known frameworks

Physicists already use “local vs. global” dual structures:

In quantum field theory QFT on curved spacetime, the local Lagrangian density is integrated over a global metric background.

In AdS/CFT correspondence, local field operators on a boundary encode the global geometry of a higher-dimensional space.

The LOA–SOA pairing is conceptually similar: it asserts that a single entropic field underlies both sides instead of treating them as independent.

Thus, the dual-structure idea highlights a deep point:

if information and entropy are the true fundamentals, then the universe’s global curvature and every local interaction are different projections of one informational geometry.  The proposal gives a language in which “quantum events” and “spacetime shape” are no longer separate categories.