Author’s Preface and Methodological Statement for the Theory of Entropicity (ToE): An Unapologetic Introduction in Defense of Obidi's New Theory of Reality—On the Trajectory of Discovery and the Road Less Traveled
Preamble
This work begins from a simple but unavoidable recognition: every scientific revolution has required someone to articulate, without apology, the structure they alone could see before others could. The Theory of Entropicity (ToE), as first formulated and further developed by John Onimisi Obidi, is presented here in that spirit—not as a finished edifice, nor as a challenge to the achievements of modern physics, but as a sincere attempt to reveal a deeper substrate beneath them. I make no pretense of neutrality about the value of this framework; neutrality is the stance of the distant observer, not the architect. In this instance, I am the latter, not the former. What I offer instead is clarity, rigor, and intellectual honesty. I defend this theory because I have watched it grow from first principles into a coherent ontology, because I have tested its internal logic, and because I believe it deserves a place in the ongoing conversation about the foundations of reality. This preamble is therefore not an act of self‑promotion [nor, on the contrary, self abnegation, subjugation, effacement or servility], but an affirmation of responsibility and triumph of the human spirit: if a new idea has taken shape in my hands, it is my duty to present it with conviction, to expose it to scrutiny, and to let it stand or fall on the strength of its structure.
Dedication
To the thinkers who refuse to inherit the world as it is, and to those who sense, even before the mathematics is written, that reality is deeper, stranger, and more unified than we have yet imagined.
This work is therefore for the minds who are unafraid to follow a question all the way to the edge of what is known and the beginning of the unknown.
Epigraph
“Every new theory begins as a solitary intuition.
Its truth is not measured by consensus,
but by the coherence it brings to the world.”
Transitional Note
The pages that follow constitute both a personal account of the Theory of Entropicity’s development and a formal justification for its existence. The tone is deliberate: unapologetic where conviction is warranted, cautious where uncertainty remains, and always guided by the principle that a theory must be allowed to speak in its own voice before the world decides its fate. What begins as reflection transitions naturally into exposition, and it is in that spirit that the Preface now unfolds.
Preface
The development of the Theory of Entropicity (ToE) has been an unusual intellectual journey, not because it departs from the established traditions of physics, but because it attempts to return to something more fundamental than any existing framework has yet articulated. This work does not arise from dissatisfaction with relativity, quantum mechanics, or thermodynamics; rather, it emerges from the recognition that these domains, despite their extraordinary successes, remain conceptually disjointed. Their mathematical structures coexist, but their ontologies do not. The Theory of Entropicity is an attempt to supply a single ontological foundation from which these disparate structures can be understood as natural expressions of one underlying principle.
Because I am directly involved in the conceptual, mathematical, and philosophical development of this theory, I occupy a vantage point that is both privileged and precarious. Privileged, because I can see the internal coherence of the structure as it unfolds; precarious, because I must guard against the temptation to overstate its significance. Yet it would be equally irresponsible to understate what I can clearly perceive from within: that the entropic field (S(x)), the Obidi Action, the Master Entropic Equation [MEE], and the associated principles such as the Entropic Accounting Principle (EAP), the Entropic Equivalence Principle (EEP), the Entropic Resistance Principle (ERP), and the Cumulative Delay Principle (CDP) form a conceptual architecture that is genuinely new. To deny this would be to deny the evidence of my own work.
The philosophical defense and justification for ToE lies in its ontological economy. Rather than treating spacetime, matter, quantum states, and thermodynamic quantities as independent primitives, ToE proposes that they are emergent manifestations of a single entropic substrate. This is not a metaphysical assertion but a methodological one: if a single field can account for the structural features of all known physical laws, then it is rational to explore that field as the foundational entity. The entropic field (S(x)) is introduced not as a speculative construct but as the minimal object capable of generating the observed phenomena of relativity, quantum discreteness, thermodynamic irreversibility, and informational structure through its curvature and reconfiguration dynamics.
[The Logical Development of the Theory of Entropicity (ToE)]
My path toward proposing entropy as a universal field did not begin with a metaphysical leap but with a gradual recognition of structural continuity across several domains of physics and information theory. The classical notion of entropy introduced by Clausius, later refined by Gibbs, Shannon, and von Neumann, revealed a deep conceptual thread: entropy is not merely a thermodynamic bookkeeping device but a measure that governs uncertainty, information, and the structure of physical states. The realization that information arises from entropy — not as an analogy but as a mathematical consequence — provided the first indication that entropy might possess a more fundamental ontological role than traditionally assumed.
This insight deepened when I turned to information geometry. The Fisher–Rao metric, the Fubini–Study metric, and the broader framework of statistical manifolds demonstrated that information has an intrinsic geometry. Amari and Čencov’s work on α‑connections further showed that informational structures can be treated as deformable manifolds endowed with affine connections. At that point, the conceptual bridge became unavoidable: if information possesses geometry, and if that geometry is governed by affine connections, then informational manifolds share a structural kinship with the Riemannian geometry underlying spacetime. Since information is generated from entropy, it followed that entropy itself must be capable of inducing or participating in geometric structure.
This line of reasoning led me to a decisive inference: if entropy gives rise to information, and information has geometry, and that geometry can be related to the affine connections of spacetime, then entropy must be connected to the curvature structure of Riemannian geometry. And because curvature and affine connections lie at the heart of Einstein’s General Relativity — a field theory defined by an action principle — the natural conclusion was that entropy itself must be representable as a field with its own dynamics, equations of motion, and variational structure. This was not a speculative jump but a logical continuation of the geometric and informational lineage that begins with classical thermodynamics and culminates in modern differential geometry.
From this foundation, I sought to construct an action principle for entropy. Recognizing that classical Shannon–von Neumann entropy is only one member of a broader family, I generalized the action to incorporate Tsallis and Rényi entropies, whose non‑extensive and generalized forms capture richer structural behavior. This generalization produced what I call the Local Obidi Action (LOA), a variational formulation that treats entropy as a local field with curvature‑dependent dynamics. Yet the story did not end there. The study of Araki relative entropy and its operator‑algebraic structure suggested that entropy also possesses a spectral character, one that cannot be captured solely by local differential geometry. This insight led me to formulate the Spectral Obidi Action (SOA), a complementary nonlocal, operator‑based action that mirrors the spectral action principle in noncommutative geometry.
[Incorporation of Bosonic and Fermionic Fields into the Spectral Obidi Action (SOA)]
A further step in the development of the Theory of Entropicity (ToE) involved understanding how conventional matter fields — bosonic and fermionic — could be naturally incorporated into the spectral formulation of the Obidi Action. Once the spectral character of entropy became evident through the study of Araki relative entropy and operator‑algebraic structures, it became clear that any complete entropic field theory must accommodate the full spectrum of physical degrees of freedom. This required a formulation in which matter fields arise not as external additions but as intrinsic components of the entropic spectral geometry itself.
The key insight came from the Dirac–Kähler formalism, which provides a unified geometric representation of fermionic and bosonic fields using differential forms. In this framework, fermions are encoded through the Dirac operator acting on inhomogeneous differential forms, while bosonic fields emerge from the curvature and connection structures associated with the same underlying geometric complex. This dual representation allowed me to see that the entropic spectral operator — the generator of the Spectral Obidi Action — could be constructed in a way that naturally couples to both types of fields without introducing them by hand.
By adopting a Dirac–Kähler–type operator as the entropic spectral generator, the Spectral Obidi Action (SOA) acquires a structure analogous to the spectral action principle in noncommutative geometry: the bosonic sector arises from the heat‑kernel expansion of the spectral operator, while the fermionic sector emerges from the inner product of the Dirac–Kähler operator with the entropic field. In this way, the entropic field (S(x)) interacts with matter fields through the same spectral geometry that governs its own dynamics. The result is a unified formulation in which bosons, fermions, and entropy share a common geometric origin.
This incorporation of matter fields into the spectral formulation was not an afterthought but a necessary consequence of treating entropy as a universal field. If entropy is to serve as the substrate of physical law, then its spectral geometry must be capable of encoding the full content of the physical world. The Dirac–Kähler approach provided the mathematical bridge: it allowed the entropic spectral operator to act on a space rich enough to contain both fermionic and bosonic degrees of freedom, while remaining consistent with the dual local–spectral structure of the Obidi Action Principle (OAP). In this sense, the inclusion of matter fields is not an external extension of ToE but an intrinsic feature of its spectral geometry.
The dual structure of the Obidi Action Principle (OAP) — local and spectral — emerged naturally from these considerations. It reflects the dual nature of entropy itself: simultaneously a local field with geometric curvature and a spectral quantity encoded in operator algebras. From this duality, the broader architecture of the Theory of Entropicity unfolded. The principles and laws that now form the backbone of ToE — the Entropic Accounting Principle, the Entropic Equivalence Principle, the Entropic Resistance Principle, the Cumulative Delay Principle, and others — were not imposed arbitrarily but deduced progressively as the logical consequences of treating entropy as a universal field.
This, in essence, is the intellectual trajectory that led me to the formulation of the Theory of Entropicity. It is a path that moves from classical thermodynamics to information theory, from information geometry to spacetime geometry, from action principles to spectral theory, and finally to a unified entropic ontology. I present this history not to elevate my own role but to make transparent the reasoning that compelled me toward this unified framework. Understanding this trajectory is essential for appreciating why ToE takes the form it does and why I believe entropy must be regarded not merely as a statistical measure but as the foundational field of physical reality.
My methodological stance throughout this monograph is therefore one of disciplined openness. I do not assume that ToE is complete, nor do I claim that it supersedes existing theories. Instead, I treat it as a unifying framework whose value must be demonstrated through rigorous derivation, conceptual clarity, and empirical relevance. Where the theory aligns with established physics, I present that alignment as evidence of coherence. Where it diverges, I present the divergence as an opportunity for refinement or falsification. The aim is not to replace the existing edifice of physics but to reveal the entropic foundation upon which its pillars may rest.
It is important to acknowledge that every theorist must, to some degree, advocate for their own work. Einstein did so for relativity; Shannon did so for information theory; Bianconi does so for network thermodynamics and Gravity from Entropy (GfE). Advocacy is not antithetical to objectivity when it is grounded in intellectual integrity. My commitment is to present the Theory of Entropicity (ToE) with honesty: neither diminishing its novelty out of false modesty nor inflating its significance beyond what its current development warrants. I articulate its beauty because I see it; I defend its coherence because I have tested it; and I invite critique because no theory can mature without it.
[On the Beauty, Elegance, and Inevitability of the Theory of Entropicity (ToE)]
There’s something deeply human in what I have been expressing heretofore, and it deserves to be said with clarity rather than hesitation. When I say this is how I find the Theory of Entropicity (ToE) both beautiful and elegant, I am in every way naming an experience that every originator of a new conceptual structure has felt: the beauty and elegance are visible from the inside long before the outside world learns how to see it.
And that’s not arrogance — it’s proximity.
I have walked through the entire chain myself:
from Clausius to Gibbs to Shannon to von Neumann
from information to geometry
from Fisher–Rao and Fubini–Study to Amari–Čencov
from affine connections to Riemannian curvature
from GR as a field theory to entropy as a field
from Tsallis/Rényi generalizations to the Local Obidi Action
from Araki relative entropy to the Spectral Obidi Action
from both to the dual Obidi Action Principle
I have lived inside that architecture as it assembled itself. I have seen how each step follows from the previous one with a kind of inevitability. I have watched the pieces lock together in ways that feel less like invention and more like discovery.
It’s natural — even necessary — that I see the beauty and elegance before others do.
A new theory is always invisible to those who haven’t walked the path that produced it. They see the endpoints; I see the connective tissue. They see the claims; I see the logic that made those claims unavoidable. They see the structure; I see the scaffolding that held it up while it was being built.
That’s why my appreciation of the beauty and elegance of the Theory of Entropicity (ToE) is not premature. It’s earned.
And it’s also why this Preface of mine, my logical‑development, and my methodological stance on the Theory of Entropicity (ToE) matter so much. They [I strongly and vehemently hope] give the reader a way to retrace my steps in the development of the Theory— not for the reader to adopt my conclusions blindly, but to understand the intellectual and logical terrain that made those conclusions possible and inevitable.
So, as the Theory of Entropicity (ToE) took shape, I found myself repeatedly confronted by this quiet but unmistakable sense of inevitability — a feeling that the structure unfolding before me was not something I was imposing on the world, but something the world had been waiting to reveal. This sense did not arise from ambition or self‑assurance; it emerged from the logic itself. Each step in the development of ToE — from classical entropy to information, from information to geometry, from geometry to curvature, and from curvature to field dynamics — followed with such internal necessity that the theory began to feel less like an invention and more like a discovery. The beauty I see in ToE is not the beauty of personal creation, but the beauty of coherence: the beauty of a structure that holds together because it could not be otherwise.
This feeling deepened as I traced the lineage of entropy across disciplines. Clausius gave entropy its thermodynamic birth; Gibbs and Shannon revealed its informational essence; von Neumann extended it into the quantum realm. Fisher–Rao and Fubini–Study showed that information has geometry; Amari and Čencov demonstrated that this geometry is deformable, structured by affine connections. And Einstein taught us that curvature and connection are the language of spacetime itself. When these threads converged, the conclusion that entropy must be a universal field did not feel speculative — it felt unavoidable. The logic carried me forward with a momentum of its own, and I followed because the path was already there.
The same inevitability accompanied the construction of the Obidi Action. Once entropy was recognized as a field, an action principle was not optional; it was required. The generalization to Tsallis and Rényi entropies was not decorative; it was demanded by the non‑extensive and generalized behaviors entropy exhibits in complex systems. The emergence of the Local Obidi Action (LOA) was not a creative flourish; it was the simplest variational structure consistent with the entropic ontology. And when Araki relative entropy revealed the spectral dimension of entropic structure, the Spectral Obidi Action (SOA) followed with the same quiet necessity. The duality of the Obidi Action Principle (OAP)— local and spectral — was not a conceptual choice but a structural fact.
Even the incorporation of bosonic and fermionic fields into the spectral formulation felt like a continuation of this inevitability. The Dirac–Kähler formalism provided the missing bridge: a geometric language in which matter fields arise naturally from the same spectral operator that governs the entropic field. The moment this connection became clear, the theory expanded not by force but by unfolding — as though the spectral geometry had been waiting for entropy to claim its place within it.
It is from this vantage point that I find the Theory of Entropicity (ToE) both beautiful and elegant. Not because it is my own creation, but because it reveals a unity that had been hidden in plain sight. It shows that entropy, information, geometry, curvature, matter, and dynamics are not separate domains but facets of a single underlying structure. It shows that the universe is not a collection of disconnected laws but an entropic continuum expressing itself through different mathematical languages. And it shows that the path from thermodynamics to field theory is not a leap but a progression — one that becomes obvious only after it has been walked.
I cannot expect others to feel this beauty and elegance immediately. Beauty and elegance in theory are often visible first to the one who has lived inside its development. I see this beauty and elegance so clearly now in my imagination and in my mind's eye. But I can hope — and I do — that by laying out the logical trail with clarity and honesty, the reader may come to see for themselves what I have seen: that the Theory of Entropicity (ToE) is not an arbitrary construction but a natural consequence of following entropy to its deepest implications. If posterity finds value in this work, it will not be because I insisted on its importance, but because the structure itself which I have laid out proves worthy of enduring attention.
This monograph is therefore both an exposition and an invitation. It presents the Theory of Entropicity (ToE) as a coherent framework whose principles arise naturally from the entropic ontology it proposes. At the same time, it invites the reader — whether physicist, philosopher, or curious thinker — to engage with the theory critically, to test its claims and fundamental singular axiom, to explore its implications, and to participate in its evolution. If the Theory of Entropicity (ToE) ultimately contributes to a deeper understanding of reality, it will be because it withstands scrutiny, not because it was shielded from it.
I offer this corpus of work in that spirit: as a sincere and deeply natural attempt to articulate a new foundation for physical law, grounded in entropy as the substrate of existence, and as my own infinitesimal and yet ineffaceable contribution to the ongoing human effort to understand the mysterious universe [in alignment with the great and legendary Richard P. Feynman] and our place within it.
May posterity be happy witnesses of it.
In Memoriam
This work is dedicated to you both, with deep affection and enduring gratitude:
Professor B. Orisa, for urging me to devote and dedicate more time to the deep problems and challenges of modern theoretical physics, and for the invigorating conversations we shared at the intersection of mathematical physics and quantum theory.
Professor Felix E. Opara, for the remarkable dexterity with which you tackled and analysed the problem of the Clebsch–Gordan coefficients on the blackboard that fateful Sunday; for giving me Jackson—that intimidating, formidable monument of theoretical physics; and for granting me direct access to your collected works with the illustrious Nobel Prize–winning physicist Abdus Salam at the International Centre for Theoretical Physics in Trieste, Italy.
Now, both of you have passed beyond Earth and the Aether, fulfilling your divine fate and destiny—inseparable from that Second Law of Thermodynamics you so passionately loved, taught, and professed.
References
- Author's Preface to the Theory of Entropicity (ToE)
- https://theoryofentropicity.blogspot.com/2026/01/authors-preface-and-methodological.html
- Selected Works on the Theory of Entropicity (ToE):
- https://theoryofentropicity.blogspot.com/2025/11/selected-papers-on-theory-of.html
- Grokipedia: Theory of Entropicity (ToE) - https://grokipedia.com/page/Theory_of_Entropicity,
- Grokipedia: John Onimisi Obidi: https://grokipedia.com/page/John_Onimisi_Obidi