Methodological Statement and Conceptual Motivation for the Theory of Entropicity (ToE)

The Theory of Entropicity (ToE), formulated by John Onimisi Obidi in 2025, is an emerging, ambitious framework in theoretical physics that redefines entropy from a statistical measure of disorder into a fundamental, continuous, and dynamic "ontological scalar field" S(x)

$S\left(x\right)$

. It proposes that entropy is the "heartbeat of existence," the foundational substrate from which space, time, gravity, and quantum mechanics emerge.

Below is a breakdown of the conceptual, methodological, and prefatory elements based on the literature published in 2025.

1. Author’s Preface & Conceptual Motivation (John Onimisi Obidi)

• The Paradigm Shift: ToE departs from the classical view that entropy is a byproduct of microscopic statistics, proposing instead that entropy is the primary field of reality—the "light itself" rather than the shadow of order.
• Decisive Step: Similar to how Einstein abandoned the ether to elevate the speed of light, ToE abandons the secondary status of entropy to elevate it to the fundamental field that drives all physical processes.
• Unification Goal: ToE aims to bridge the gap between thermodynamics, general relativity, and quantum mechanics, which are typically separated by their treatment of time and irreversibility.
• Core Philosophy: The universe is not a machine but a living field of entropy, perpetually updating itself. Matter is interpreted as a localized, compactified, and stable configuration of the entropic field (
  

  $S\left(x\right)$
  ).

2. Methodological Statement: The "How" of ToE

The ToE operates through a rigorous, newly developed mathematical and variational framework:

• The Obidi Action I_sg(
  

  $I[S,g]$
  ): This is the core variational principle, defined as a spacetime action functional, which couples the entropy field
  

  $S\left(x\right)$
  to gravity.
  • Local Obidi Action (LOA): Handles differential, local field dynamics of entropy in spacetime, yielding the Master Entropic Equation (MEE).
  • Spectral Obidi Action (SOA): Uses spectral traces of an "entropy operator" (akin to Connes' spectral action) to impose global constraints on the system.
• Information-Geometric Foundation: ToE connects informational entropy to physical geometry by integrating Fisher–Rao and Fubini–Study metrics through the Amari–Čencov alpha-connection.
• The Vuli–Ndlela Integral: A reformulation of Feynman’s path integral that introduces irreversibility and temporal asymmetry directly into quantum mechanics by weighting paths based on entropy flow.
• Derivative Approach: Rather than postulating physical laws (like the constant speed of light), ToE derives them as "entropic inevitabilities" arising from the conservation of entropy and the resistance of systems to entropy flux.

3. Key Principles and Claims

• The No-Rush Theorem: A "fundamental, non-zero duration" limit on all physical interactions, based on the principle that "nature cannot be rushed". It states that the entropic field takes time to process any change.
• Speed of Light (
  

  $c$
  ) as a Rate: The speed of light is not a fundamental postulate, but the maximum rate of entropic rearrangement—the fastest the universe can process information.
• Entropic Resistance Principle (ERP): Explains mass increase and time dilation as a consequence of the energy required to move through the entropic field.
• Emergent Spacetime: Spacetime curvature is not caused by mass but by entropy gradients, meaning geometry is emergent, not fundamental.
• Self-Referential Entropy (SRE) & Consciousness: Introduces the "SRE Index," a measure of consciousness based on a system’s internal-to-external entropy flow, proposed as a solution to the "hard problem" of consciousness.

4. Comparison with Other Theories

Unlike other "entropic gravity" models (e.g., Verlinde's), which treat gravity as an entropic force, ToE establishes entropy as a fundamental field that entirely replaces spacetime, with gravity emerging as a result of that field.

• Status: The theory was in active development and publication during 2025 (e.g., in Authorea, Cambridge Engage, and MDPI), representing a "highly audacious and radical" new approach that requires further peer review and testing.