Communications Between Daniel Moses Alemoh and John Onimisi Obidi on the Foundations and Formulation of the Theory of Entropicity (ToE): Dialogues on a New Theory of the Foundation of Modern Theoretical Physics—Part II

Preamble 

Scientific revolutions often germinate through private correspondence rather than polished manuscripts.  Between 2025 and 2026 John Onimisi Obidi shared a developing theoretical program with Daniel Moses Alemoh.  Obidi proposed that entropy is not a derivative thermodynamic bookkeeping quantity but the primary field from which space, time, matter and information emerge.  This radical inversion of twentieth‑century physics treats entropy as a dynamical scalar field S(x) defined on an entropic manifold.  Obidi and Alemoh debated how to formalize this idea, how to reinterpret constants like the speed of light, how to explain cosmic expansion, and how to derive known physics from an entropic action.  This article reconstructs those dialogues into a structured review, placing them in the context of existing entropic theories and citing publicly available sources.  We argue that the Theory of Entropicity (ToE) represents a bold attempt to rebuild modern physics on an informational foundation comparable in ambition to Einstein’s elevation of c to a universal postulate.

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1 Introduction

Correspondence has long nurtured scientific innovation.  Letters between Newton and Hooke, Einstein and Besso, or Bohr and Schrödinger often contained nascent ideas that later reshaped physics.  In that tradition, the exchanges between John Onimisi Obidi and Daniel Moses Alemoh trace the gestation of the Theory of Entropicity (ToE).  ToE calls for “abandoning the view of entropy as a secondary, statistical by‑product and instead elevating it to the status of a fundamental field”.  In analogy with Einstein’s decisive step of elevating the speed of light c, ToE posits a universal entropic field S with its own dynamics.  The central claim is that the geometry of space, the flow of time and the dynamics of motion are manifestations of entropy gradients rather than primitive structures.  This inversion implies that constants, interactions and even measurement emerge from the entropic field’s behaviour. (encyclopedia.pub)

Alemoh’s role was not merely receptive; he raised penetrating questions about the consistency of this framework.  In particular he asked how a theory in which spacetime is emergent could reconcile a finite light‑speed limit with the observed superluminal recession of galaxies, and how ToE could reproduce known physics.  The following sections organize the core themes of their correspondence and amplify them using published expositions of ToE and related entropic models.

2 The Entropic Field: Ontological Foundation

Classical physics begins with geometry or quantum fields as ontological primitives.  By contrast, ToE begins with a scalar entropic field defined on an entropic manifold S.  This field is continuous, differentiable and dynamically evolving.  Each point of the manifold has a real‑valued entropic density representing intrinsic “ontological density,” configurational multiplicity, geometric potential and information substrate.  The entropic field’s gradients behave like forces and determine “entropic geodesics,” while higher derivatives encode curvature‑like responses.  In effect, the entropic field is the substrate from which geometry, forces and information flow are derived. (theory-of-entropicity-toe.pages.dev)

The entropic field has both local and non‑local contributions.  Local variations determine immediate dynamics, while non‑local structure governs global coherence.  These features allow ToE to account for both short‑range interactions and large‑scale cosmological phenomena within the same framework.(theory-of-entropicity-toe.pages.dev)

3 The Obidi Action and the Master Entropic Equation

Correspondence between Obidi and Alemoh repeatedly returned to the need for a rigorous mathematical formalism.  In ToE the dynamical laws arise from the Obidi Action—an entropic analogue of the Einstein–Hilbert action.  The Obidi Action is a variational principle which encodes the dynamics of the entropy field S.  Varying this action yields the Master Entropic Equation (MEE) or Obidi Field Equations (OFE).  These equations play the role that Einstein’s field equations play in general relativity, governing how entropy gradients evolve and couple to geometry, matter and information.  From the MEE follow secondary structures: (encyclopedia.pub)

Entropic geodesics—natural paths in the entropic manifold along which systems evolve.

Entropic potential equation—a relation governing the manifestation of entropic forces.

Unlike Einstein’s equations, which admit closed‑form solutions in highly symmetric situations, the ToE field equations are generally approached via iterative methods.  This reflects the inherently probabilistic and information‑theoretic nature of entropy; solutions are successive refinements rather than static metrics.  The iterative character underscores ToE’s view that physical laws are emergent equilibria of continuous entropic computation rather than fixed constraints. (encyclopedia.pub)

4 Iterative Nature of the OFE and the Vuli–Ndlela Integral

The OFE describe the continuous evolution of the entropy field, not the curvature of a fixed spacetime.  They imply that entropy is not a passive measure but an active generative principle that reorganizes reality.  Solving the OFE requires starting from an initial informational configuration and allowing it to evolve through successive entropy updates.  Each iteration yields a more stable entropic structure, analogous to Bayesian updating.  In this perspective, the universe is an ongoing computation: it never “arrives” at a configuration but continuously recalculates its entropic state. (encyclopedia.pub)

The Vuli–Ndlela Integral generalizes Feynman’s path integral to entropy.  Instead of summing over mechanical trajectories, it sums over entropic configurations of the universe’s informational state.  Each configuration is weighted by both a causal phase and an entropic attenuation that accounts for irreversible growth or redistribution of entropy.  Information geometry provides the natural mathematical setting: probability distributions form a curved manifold whose curvature is interpreted physically as gravitational, electromagnetic and quantum phenomena.  Hence ToE unites path integrals and information geometry, expressing physical evolution as an unending dialogue between entropy, information and geometry. (encyclopedia.pub)

5 Dialogues on the Speed of Light and Cosmic Expansion

A key theme in Alemoh’s correspondence concerned the interpretation of the speed of light.  Standard physics treats as a fundamental invariant entering Lorentz symmetry.  ToE, however, interprets as the maximum rate at which the entropic field can reorganize information.  This finite rate governs causal interactions and becomes the emergent constant observed in relativity.  Thus is a property of the present entropic regime rather than an immutable number.  If the dynamics of the entropic field were different in another epoch or region, the effective value of could differ. (encyclopedia.pub)

Alemoh asked how this interpretation can coexist with super‑luminal cosmic expansion.  In standard cosmology, galaxies recede faster than because the metric expands; there is no violation of causality.  ToE explains this by distinguishing two sectors:

Local dynamical sector—internal propagation of disturbances within the entropic field.  Signals, particles and causal influences are limited by the finite entropic redistribution rate.

Global background sector—evolution of the entropic manifold itself.  Cosmic expansion is interpreted not as motion through pre‑existing space but as the growth or extension of the entropic manifold.  Hence recession speeds may exceed because the “medium” is expanding; this does not transmit information faster than.  This distinction parallels Daniel Alemoh’s analogy: light is the fastest ripple through the field, while expansion is the field itself increasing its extent (as described in Obidi’s replies).

In these dialogues Obidi emphasized that ToE must formalize this separation.  The OFE and Vuli–Ndlela Integral treat the background evolution as part of the entropic dynamics.  Locally, the finite entropy redistribution rate enforces relativity; globally, entropic growth accounts for cosmological expansion.  Thus the entropic speed limit remains intact while ToE accommodates super‑luminal recession.  External entropic theories support this view.  A mainstream news report on Ginestra Bianconi’s work notes that gravity can be derived from an entropic action coupling matter fields with geometry, underscoring that entropic actions can produce gravitational dynamics without requiring a fixed spacetime.  ToE extends this insight by providing both local and spectral Obidi Actions that yield the Master Entropic Equation, entropic geodesics and a unified description of gravity, time, quantum processes and information geometry. (popularmechanics.com), (cambridge.org)

6 Integration with External Entropic Paradigms

While ToE is original, it connects to broader efforts to derive spacetime and gravity from entropy.  Verlinde’s entropic gravity, Bianconi’s quantum relative entropy, and emergent time proposals all suggest that gravity and time may have entropic origins.  A popular exposition notes that gravity can emerge from quantum relative entropy and an entropic action.  These ideas show that entropic considerations can lead to Lorentz‑symmetric dynamics and even cosmological constants.  ToE goes beyond these frameworks by elevating entropy to a universal field and introducing the Obidi Action and Vuli–Ndlela Integral.  In this sense, ToE can be seen as unifying and extending entropic gravity programmes by providing both a local variational principle and a spectral variational principle.(popularmechanics.com), (cambridge.org)

The ToE programme also resonates with information geometry.  In information geometry the manifold of probability distributions has a natural curvature, and distances measure distinguishability.  The entropic field’s curvature in ToE plays an analogous role, linking the geometry of information to physical phenomena.  This connection suggests that the entropic manifold might correspond to the statistical manifold underlying quantum states and thermodynamic ensembles.  Thus ToE offers a conceptual bridge between physics and inference. (encyclopedia.pub)

7 Concluding Reflections and Future Work

The dialogues between Daniel Moses Alemoh and John Onimisi Obidi exemplify how critical questioning refines speculative theories.  Alemoh’s insistence on clarifying the status of c, the nature of cosmic expansion, and the formal foundations of ToE drove Obidi to sharpen his formulations.  The resulting theory is ambitious: it posits that entropy is the heartbeat of existence, not a measure of disorder; it proposes an entropic field whose gradients and curvature generate forces and geometry; it introduces an Obidi Action yielding a Master Entropic Equation analogous to Einstein’s equations; and it generalizes path integrals through the Vuli–Ndlela Integral (VNI).  These elements suggest a new foundation for physics grounded in information and irreversibility. (encyclopedia.pub), (theory-of-entropicity-toe.pages.dev)

However, ToE remains in a formative stage.  Major challenges include: deriving Lorentz symmetry and known field theories from the entropic field; computing testable predictions; understanding how quantum measurement arises; and integrating the theory with established thermodynamics.  The iterative character of the OFE implies that approximate numerical schemes will be needed.  Furthermore, philosophical questions—such as whether time becomes an emergent ordering of entropic updates—require careful analysis.

Despite these challenges, the ToE correspondence illustrates a bold ontological courage: the willingness to question entrenched primitives and to propose that reality is fundamentally informational.  If future work can bridge ToE with empirical data and established physics, the entropic field may one day stand alongside the speed of light as a new pillar of natural philosophy.

References

J. O. Obidi, Theory of Entropicity (ToE): Chapter 2 – The Entropic Field, 2025–2026, describing the entropic field as a continuous, differentiable, dynamically evolving scalar whose gradients and curvature generate forces and geometry.

theory-of-entropicity-toe.pages.dev

theory-of-entropicity-toe.pages.dev

J. O. Obidi, Theory of Entropicity (ToE): Path to Unification of Physics, Encyclopedia MDPI, 2025.  The article proposes elevating entropy to a universal field, analogous to Einstein’s elevation of c; it introduces the Obidi Action, Master Entropic Equation and entropic geodesics.(encyclopedia.pub)

J. O. Obidi, The Theory of Entropicity Goes Beyond Holographic Pseudo‑Entropy, Cambridge Open Engage, 2026.  The abstract emphasises that ToE treats entropy as the fundamental physical field equipped with local and spectral Obidi actions, producing a unified description of gravity, time, quantum processes and information geometry. (cambridge.org)

E. Rayne, “A New Theory Says Gravity May Come From Entropy—Which Could Lead to a Unified Theory of Physics,” Popular Mechanics, 20 January 2026.  The article quotes Ginestra Bianconi: “Gravity is derived from an entropic action coupling matter fields with geometry”—an external perspective supporting entropic action approaches. (popularmechanics.com)

J. O. Obidi, Theory of Entropicity (ToE): Information Geometry and the Vuli–Ndlela Integral, Encyclopedia MDPI, 2025.  Discusses how the Vuli–Ndlela Integral sums over entropic configurations weighted by causal phases and entropic attenuation, connecting ToE to path integrals and information geometry. (encyclopedia.pub)

This document synthesizes the key themes from your discussions with Daniel Moses Alemoh on the Theory of Entropicity, situating them within broader entropic and information-theoretic frameworks while retaining the conversational spirit of your exchanges. It includes citations to publicly available sources that support and expand upon the ideas explored between Daniel Moses Alemoh and John Onimisi Obidi on the foundations and formulation of the Theory of Entropicity (ToE).