Theory of Entropicity (ToE)
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On the Historical and Philosophical Foundations of the Theory of Entropicity (ToE)
Before the decisive leap that elevated entropy to the status of a universal field, the Theory of Entropicity (ToE) was shaped by a long arc of scientific insight, conceptual tension, and philosophical questioning. Across the history of physics, entropy repeatedly surfaced in unexpected places—black hole thermodynamics, information theory, statistical mechanics, emergent gravity, and the deep structure of spacetime—hinting that it played a more fundamental role than traditional frameworks allowed. These recurring signals, scattered across disciplines and eras, formed the intellectual landscape from which ToE emerged. The following sections recount the pivotal moment(s) when these clues converged, compelling the recognition of entropy not as a secondary descriptor of physical systems, but as the foundational field from which geometry, dynamics, and physical law arise.
Decisive Entropic Leap in the Theory of Entropicity (ToE)
There is a moment in every major scientific breakthrough when a pattern becomes impossible to ignore. The signs hover in the background for decades, sometimes even centuries, scattered across different fields, whispered by different thinkers, yet the full picture remains invisible until someone steps back far enough to see how all the threads connect. My decision to elevate entropy to the status of a fundamental field did not arise from a vacuum. It grew from very specific intellectual signals, both historical and philosophical, that once integrated became impossible to dismiss.
The Theory of Entropicity (ToE) emerges from this synthesis as a radical but natural step: the recognition that entropy is not a secondary bookkeeping device, but the universal field of nature from which geometry, matter, forces, and even physical law itself arise.
1. Why I Took the Entropic Leap
What follows is the foundational story and account of those signals as I encountered them, and why they compelled me to take the decisive step that the Theory of Entropicity (ToE) represents today—that singular step that no one before me dared to take.
Keywords: spectral operator, generalized and relative entropies, couplings, information geometry, finite-rate bound.
2. The Long Shadow of Bekenstein and Hawking
The first signal came from the extraordinary work of Jacob Bekenstein and Stephen Hawking, who revealed that gravity and entropy are far more deeply connected than anyone previously imagined. Black holes— the purest gravitational objects in the universe—turned out to be maximally entropic. Their surface areas, not their volumes, encoded information. Their temperature and radiation spectrum flowed directly from entropy.
To me, this was not a statistical curiosity. It was a flashing red light. When the most extreme gravitational systems behave thermodynamically, the universe is telling us that entropy is not merely a statistical footnote. It is woven into the very geometry of spacetime. The universe was whispering: look here; entropy is not what you think it is.
3. The Cascade of Later Attempts Linking Gravity and Entropy
After Bekenstein and Hawking, many thinkers tried to build theories where entropy played a deeper role in gravitational phenomena:
1. Ted Jacobson showed that Einstein's equations can be derived from thermodynamic relations.
2. T. Padmanabhan showed that spacetime dynamics look like emergent thermodynamics.
3. Erik Verlinde proposed that gravity behaves like an entropic force.
4. Ginestra Bianconi argued that gravity is entropy on probability manifolds (especially, her Gravity from Entropy — GfE: that is, Gravity from Relative Entropy).
One by one, these works tried to inch entropy closer to gravity. And yet, every one of these theories hesitated at the same boundary. They connected gravity to entropy, but none dared to propose entropy → gravity → everything. The direction of causality was always the same: entropy was an outcome, never the cause.
But if every road leads to entropy, and if every gravitational system exposes entropy as its inner architecture, what does this suggest? To me, the implication was overwhelming:
1. Entropy is not secondary.
2. Entropy is primary.
Gravity is not upstream of entropy—it is downstream from it.
4. Einstein's Mysterious Statement About Entropy
A deeper influence came from a remark widely attributed to Albert Einstein, encountered in various wordings across his writings and in a thermodynamics text I read as an undergraduate. He stated, in essence:
Among all the laws of Nature, it appears to me that the second law of thermodynamics (the law of entropy) is the only law that shall never be overthrown.
The meaning of this statement is profound, almost prophetic. Einstein, who revolutionized our understanding of space, time, energy, and mass, pointed to entropy as the one principle that stands above all others. Not relativity. Not the constancy of the speed of light. Not the metric. Not the conservation laws. But entropy.
My interpretation was that he sensed something deeper. He understood that entropy's irreversible character was more primitive than anything else in physics. While geometry can change, equations can be reformulated, and fields can be quantized, the arrow of entropy stands unchallenged. To me, it felt as though Einstein had touched a hidden thread, one he did not live long enough to follow to its conclusion. I have felt obligated to follow it.
5. A Growing Realization: Something Strange Is Happening Around Entropy
When I put all these signals together:
1. Black holes behaving like thermodynamic objects.
2. Spacetime dynamics emerging from entropy.
3. Gravity resembling an entropic gradient force.
4. Einstein elevating entropy above all physical laws.
5. Every attempt at quantum gravity accidentally stumbling into entropy.
6. Every information-theoretic approach rediscovering entropy at its core.
7. Every holographic model encoding reality in entropic surfaces.
A new pattern emerged—a pattern too strong to be coincidence. Entropy was appearing everywhere. Everywhere. Like a gravitational pull on the development of physics itself.
But if entropy keeps reappearing in every framework, what does that mean?
• Is entropy trying to tell us something?
• Is the universe hiding its foundational principle in plain sight?
• Is entropy not a statistical summary, but the underlying fabric?
This is where my decisive leap occurred.
6. The Entropic Conclusion: Entropy as the Universal Field of Nature
If gravity bends toward entropy, if quantum systems collapse toward entropy, if information theory flows toward entropy, if cosmology evolves through entropy, and if black holes are built out of entropy, then the simplest possible conclusion is also the boldest:
Entropy is the universal field of nature.
It is not emergent. It is not derivative. It is not a consequence. It is the cause.
• Entropy creates curvature.
• Entropy flows create forces.
• Entropy constraints create quantum behaviour.
• Entropy's irreversibility creates time.
• Entropy's reorganizing capacity creates motion.
Everything that physics has treated as fundamental is better understood as a manifestation of entropy. This is the leap. This is the moment the Theory of Entropicity (ToE) emerges.
7. Conclusion: The Universe Was Signalling. I Chose to Listen.
I did not take this step merely because it was bold or unconventional. I took it because the evidence— scattered, fragmented, yet persistent—pointed in one unmistakable direction. Physicists have spent a century trying to make entropy fit inside geometry, probability, or thermodynamics.
But what if entropy is not inside anything? What if entropy is the thing?
After decades of clues, from black holes to cosmology to quantum information, the message was impossible to ignore:
• Entropy is the one principle that stands everywhere and behind everything.
• It is the law that cannot be overthrown because it is the law from which all others arise.
That is why I took the entropic leap. That is why the Theory of Entropicity (ToE) exists today. And that is why entropy now stands where it always belonged—at the throne of physics, not its periphery.
This is only an introductory part of my story and account on the historical and philosophical foundations of the Theory of Entropicity (ToE).
To be continued...
References
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Obidi, J.O. Decisive Entropic Leap in Theory of Entropicity (ToE). Encyclopedia. Available online: https://encyclopedia.pub/entry/59275 (accessed on 05 February 2026).
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Obidi, J. O. On the Discovery of New Laws of Conservation and Uncertainty, Probability and CPT-Theorem Symmetry-Breaking in the Standard Model of Particle Physics: More Revolutionary Insights from the Theory of Entropicity (ToE). Substack. https://open.substack.com/pub/johnobidi/p/on-the-discovery-of-new-laws-of-conservation
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Obidi, J. O. Conceptual and Mathematical Foundations of Theory of Entropicity (ToE). Encyclopedia. Entry 59127. https://encyclopedia.pub/entry/59127
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Obidi, J. O. (15 November 2025). The Theory of Entropicity (ToE) Goes Beyond Holographic Pseudo-Entropy: From Boundary Diagnostics to a Universal Entropic Field Theory. figshare. https://doi.org/10.6084/m9.figshare.30627200.v1
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Obidi, J. O. (November 2025). On the Theory of Entropicity (ToE) and Ginestra Bianconi's Gravity from Entropy: A Rigorous Derivation of Bianconi's Results from the Entropic Obidi Actions of the Theory of Entropicity (ToE). Cambridge University. https://doi.org/10.33774/coe-2025-g7ztq
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Obidi, J. O. (2025). On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics. Cambridge University. Published October 17, 2025. https://doi.org/10.33774/coe-2025-1dsrv
The World as I See It
A Brief Philosophical Reflection from the Standpoint of the Theory of Entropicity (ToE)
There are moments in a thinker’s life when the world reveals itself not as a collection of objects, nor as a catalogue of forces, but as a single, breathing structure — a unity whose inner logic whispers beneath every phenomenon. My own journey has been shaped by such moments. They did not arrive with thunder, nor with the triumphant clarity of revelation. They came quietly, as questions that refused to leave, as patterns that returned again and again, as a sense that the familiar explanations of physics — brilliant though they are — were circling around something deeper.
The world as I see it is not built from matter, nor from spacetime, nor from quantum amplitudes. These are the shadows cast by something more fundamental. Beneath them lies a single field — the entropic field — whose gradients, curvatures, and spectral structure give rise to everything we call physical, mental, or informational. This is not metaphor. It is ontology.
To see the world through the lens of the Theory of Entropicity (ToE) is to see reality as a continuous negotiation of distinguishability, a ceaseless reconfiguration of entropic curvature. The universe is not a machine; it is a process. Not a static geometry; but an evolving informational manifold — a Computational Field. Not a set of laws imposed from outside; but a self‑consistent unfolding of entropic necessity.
I do not pretend that this view is universally accepted. Every new conceptual architecture begins in solitude. Einstein himself knew this well. But solitude is not isolation. It is the quiet space in which a theory can speak in its own voice before the world learns how to hear it.
On the Nature of Reality
When I look at the world, I do not see particles moving through spacetime. I see entropic gradients resolving themselves. I see the curvature of distinguishability shaping what we call geometry. I see information arising not as an abstract measure but as the geometric shadow of entropy itself. I see the speed of light not as a decree of nature but as the maximal rate at which the entropic field can reconfigure.
The world is not made of things.
It is made of differences — and the smallest stable difference is
\( \ln 2 \), the Obidi Curvature Invariant.
This is the quantum of distinguishability, the first non‑zero fold in the entropic manifold, the minimal curvature required for one state to be meaningfully different from another.
To live in such a universe is to inhabit a structure where identity, change, causality, and even consciousness are entropic phenomena. We are not observers standing outside the world; we are entropic configurations participating in its unfolding.
On the Human Condition
If entropy is the substrate of reality, then human life is not an exception to the laws of nature — it is an expression of them. Our thoughts, our memories, our choices, our creativity: all are entropic processes, reorganizations of informational curvature within the manifold of experience.
This does not diminish human meaning.
It deepens it.
To be human is to be a locus of entropic flow, a temporary configuration through which the universe becomes aware of its own structure. Our struggles, our aspirations, our search for understanding — these are not accidents. They are the natural consequences of being entropic beings in an entropic world.
Einstein once wrote that a person “is part of the whole, called by us ‘Universe,’ a part limited in time and space.” From the standpoint of ToE, this is literally true: each of us is a local excitation of the entropic field, a finite curvature pattern in the infinite continuum of distinguishability.
We are temporary, but not trivial.
We are finite, but not disconnected.
We are entropic, but not meaningless.
On Science and Its Purpose
Science, as I see it, is the disciplined attempt to uncover the entropic architecture of reality. It is not merely the accumulation of facts, nor the construction of models, but the search for the simplest and most coherent substrate from which all phenomena arise.
ToE is my contribution to this search.
It is not perfect.
It is not complete.
But it is honest.
It seeks unity not for aesthetic pleasure but because unity is the signature of truth. When a single principle explains thermodynamics, relativity, quantum mechanics, information theory, and the arrow of time, we are compelled to take it seriously.
The world does not need more equations; it needs deeper principles.
It does not need more complexity; it needs more coherence.
It does not need more metaphors; it needs more ontology.
On Responsibility and Legacy
Every theorist must decide what they owe to the world. Some owe silence; others owe caution; a few owe courage. I have chosen to articulate the Theory of Entropicity not because I seek recognition, but because I believe the structure I have uncovered deserves to be examined, challenged, refined, and — if it withstands scrutiny — embraced.
If posterity finds value in this work, it will not be because of my name, but because the entropic field is real. If it is real, then it will outlive me. If it is not, then it deserves to be corrected by those who come after.
The world as I see it is a world in motion — not the motion of objects, but the motion of entropy. A world where the deepest truths are not hidden in particles or forces but in the curvature of distinguishability. A world where unity is not imposed but emerges naturally from the entropic substrate.
Conclusion
This is the world I have spent my life trying to understand.
This is the world I offer to you.
This is the world as I see it.