Originality of the Theory of Entropicity (ToE): Declaration of a Universal Entropic Field and the Alpha Connection of Information Geometry as Spacetime Generator and as the Geometric Tuning Parameter that Induces the Physical Arrow of Time 

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Executive Introduction

No single researcher before the Theory of Entropicity (ToE) has achieved all three of the following simultaneously as a single physical principle:

1. Using the α-connection as a unifying geometric bridge between Fisher–Rao (classical) and Fubini–Study (quantum) metrics,
2. Interpreting generalized entropy (e.g., Tsallis/q-entropy) as physical curvature of an entropic manifold, and
3. Deriving the arrow of time as an intrinsic geometric property of that entropic manifold rather than as a statistical or boundary-condition artifact.

However—this is crucial—each component exists in the literature separately, sometimes very deeply.
What ToE does is re-ontologize and fuse them into a single dynamical framework.

That fusion is original in scope and intent, even though it uses known mathematics.

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Let’s analyze this statement carefully

In ToE, we find:

the α-connection in ToE is the geometric bridge that (i) unifies Fisher–Rao and Fubini–Study metrics, (ii) ties generalized entropy (via [q]) to curvature, and (iii) makes the arrow of time a property of the entropic manifold itself.

We will examine each clause historically for the purpose of giving our readers a good grounding pertaining to the undeniable audacity and yet originality of Obidi's Theory of Entropicity (ToE).

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(i) Unifying Fisher–Rao and Fubini–Study metrics via α-connections

What is already known

• Amari & Nagaoka (2000) developed α-connections in information geometry.
• Fisher–Rao geometry is classical (probability distributions).
• Fubini–Study geometry is quantum (projective Hilbert space).
• Petz, Gibilisco, Brody, Hughston showed relations between:
  • quantum Fisher information,
  • monotone metrics,
  • and Fubini–Study–type structures.

There are also papers showing that α = ±1 connections correspond to specific dualistic structures.

✅ So the mathematical unification exists.

What ToE does differently

• In standard work, α-connections are:
  • mathematical tools,
  • used for estimation, inference, or state distinguishability.
• In ToE:
  • the α-connection is treated as a physical connection on a real entropic field,
  • not just on probability spaces or state manifolds.

📌 Originality here is not the math, but the ontology:
ToE says this geometry is what spacetime and dynamics emerge from. This is an extraordinary push and proposition in the annals of Modern Theoretical Physics.

That claim is not present in Amari, Petz, or quantum information geometry.

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(ii) Generalized entropy (q-entropy) as curvature

What is already known

• Tsallis entropy introduces a deformation parameter q.
• In information geometry:
  • q-exponentials appear naturally,
  • α-connections are related to q via α = 1 − q (or similar mappings).
• Authors like Naudts, Eguchi, Ohara studied deformed exponential families and geometry.

✅ So q-geometry is known mathematically.

What ToE adds

• In standard treatments:
  • q measures non-extensivity or correlations,
  • geometry is descriptive, not causal.
• In ToE:
  • q is promoted to a curvature-control parameter of a physical entropic field,
  • curvature generates forces, time delay, and geometry.

📌 No prior framework treats q-entropy as literal physical curvature generating spacetime and dynamics.

This is a conceptual escalation, not just reinterpretation. Again, this is a profound conceptual leap of the human imagination.

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(iii) Arrow of time as intrinsic geometry of the entropic manifold

This is the most important part.

What physics already has

• Boltzmann: arrow of time from probability.
• Prigogine: irreversible structures.
• Penrose: Weyl curvature hypothesis.
• Carroll: low-entropy initial condition.
• Quantum information: entanglement growth.
• Thermodynamics: coarse-graining + statistics.

All of these:

• rely on initial conditions,
• or statistical arguments,
• or coarse graining,
• or observer dependence.

❌ None of them make time asymmetry a connection-level geometric property.

What ToE claims, posits and declares 

• The α-connection is not symmetric under dual reversal.
• The entropic manifold has built-in directional curvature flow.
• Time asymmetry appears even before:
  • observers,
  • coarse graining,
  • ensembles.

📌 This move—placing the arrow of time in the geometry itself—is genuinely rare. This most innovative leap of the imagination is purely in a class of its own.

The closest analogs:

• thermodynamic length (Crooks),
• information geometry of dissipation,

but even those do not claim time as a fundamental geometric direction of the universe.

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So is ToE original?

Precise verdict

• ❌ Not original in mathematical ingredients:

  • α-connections,
  • Fisher–Rao,
  • Fubini–Study,
  • q-entropy,
  • relative entropy curvature.

• ✅ Original in synthesis and ontological claim and proposition:

  • entropy as a physical field,
  • α-geometry as spacetime-generating,
  • time arrow as geometric inevitability.

This is similar to Einstein:

• Minkowski geometry existed,
• Lorentz transformations existed,
• but spacetime geometry as physical reality describing gravity was new.

This Einsteinian trajectory of generalization and declaration is precisely what John Onimisi Obidi has undertaken and followed through in generalizing and declaring that entropy is a universal field and that the alpha connection geometry of information geometry is an asymmetry that is physically and intrinsically [linked to] the arrow of time itself. In a clear brief, this is Obidi's originality.

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Conclusion 

ToE's Primal Claim 

The Theory of Entropicity is the first framework to interpret the α-connection of information geometry as a physical connection on a universal entropic field, unifying classical and quantum information metrics and embedding the arrow of time directly into the geometry of reality.

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Closure 

Therefore, ToE's insight is not a rediscovery; it is a re-foundational move.
ToE has not invented new mathematics—it changes what the mathematics is about with extraordinarily broad and irrefutable unification undercurrents in physical terms.

That is exactly how major theoretical shifts in science, and of course in physics, occur historically.