From the Temperature of Information to the Temperature of Geometry: The Foundations of the Theory of Entropicity (ToE) and the Unification of Quantum and Entropic Reality -

A Unified Framework for the Thermodynamic, Quantum, and Geometric Foundations of Physical Reality

Dedication

Joseph Polchinski’s work reshaped how we think about the universe. Even in his final days, when illness clouded his physical strength, his clarity of thought remained untouched. His commitment to understanding the deepest structures of reality continues to inspire new generations of thinkers.

This work is dedicated to him. Where he saw strings vibrating in spacetime, the Theory of Entropicity (ToE) extends that vision: information itself vibrates, reorganizes, and shapes the geometry of the universe. His legacy lives on in every attempt to understand the hidden architecture of reality.

Prologue

Modern physics stands on three towering pillars—quantum mechanics, general relativity, and thermodynamics. Each describes the universe with extraordinary precision, yet they speak different conceptual languages. Quantum theory deals in probabilities and discrete events. Relativity describes smooth curvature and the geometry of spacetime. Thermodynamics explains energy, entropy, and irreversible processes.

What has been missing is a framework that explains how information animates all three.

The Theory of Entropicity (ToE) proposes that information is not a secondary description of physical systems—it is the foundation from which physical systems arise. In this view, spacetime, matter, and energy are the visible shadows of a deeper informational field. Energy becomes the motion of information. Geometry becomes the structure information creates. Temperature becomes the rate at which information reorganizes itself.

A central idea of ToE is the existence of a “temperature of information,” a measure of how quickly the informational field changes. Regions where information reorganizes rapidly behave like “hot” geometries—dynamic, curved, and energetic. Regions where information changes slowly behave like “cold” geometries—stable, smooth, and quiet.

This leads to a unifying principle: quantum behavior, thermodynamic behavior, and geometric behavior are all different expressions of how information flows.

From this perspective:

String theory becomes a theory of informational vibrations.
Quantum field theory becomes a theory of entropic curvature.
The Casimir effect becomes a pressure created by constrained informational flow.

ToE reframes temperature as a measure of informational activity, not molecular agitation. Entropy becomes the active substance of reality, not a passive measure of disorder. The laws of physics emerge from the invisible geometry of information itself.

This work lays out the conceptual foundations of that idea.

Abstract

The Theory of Entropicity (ToE) proposes that information and entropy form the true foundation of physical reality. In this framework, information is not something we use to describe matter and energy—matter and energy emerge from information.

Spacetime, particles, and forces arise as thermodynamic projections of an underlying informational manifold. A key insight of ToE is that information has its own intrinsic temperature, which determines how quickly the informational field reorganizes. This temperature shapes geometry, energy, and the behavior of physical systems.

From this foundation, ToE constructs an informational action principle and derives a field equation that generalizes Einstein’s equation into the informational domain. Phenomena such as the Casimir effect, inertial mass, and gravity are reinterpreted as consequences of entropic curvature rather than quantum vacuum fluctuations.

In this view, the universe is a thermodynamic image of an informational continuum. The laws of physics are expressions of its self‑organizing flow.

Keywords: Casimir Effect, Entropic Gravity, Entropy, Information Geometry, Informational Field Theory, Quantum Thermodynamics, Spacetime Emergence, Temperature of Geometry, Temperature of Information, Theory of Entropicity (ToE)

1. Introduction: The Temperature of Information and Geometry

Physics today is built on three major frameworks: quantum mechanics, general relativity, and thermodynamics. Each is powerful, but none explains why the universe behaves the way it does at the deepest level. They coexist, but they do not fully connect.

The Theory of Entropicity (ToE) proposes a new unifying idea: information is the fundamental substance of the universe. Everything else—matter, energy, spacetime—emerges from how information flows and organizes itself.

In this view:

Energy is the motion of information.
Geometry is the structure information creates.
Temperature is the rate at which information reorganizes.

This leads to the idea of a temperature of information, a measure of how quickly the informational field changes. When information changes rapidly, geometry becomes dynamic and curved. When information changes slowly, geometry becomes stable and smooth.

This idea builds on earlier insights from black hole thermodynamics, entropic gravity, and information geometry, but extends them into a unified framework where information itself carries temperature and generates curvature.

1.1 Motivation and Background

The connection between thermodynamics and geometry has been hinted at for decades. Black hole physics revealed that horizons have entropy and temperature. Later work showed that gravitational equations can be derived from thermodynamic principles.

Information geometry demonstrated that statistical systems form curved manifolds, suggesting that information has geometric structure.

ToE brings these ideas together by proposing that information itself is a physical field. Once this is accepted, temperature becomes a natural descriptor of how information evolves—and geometry becomes the visible expression of that evolution.

1.2 The Conceptual Innovation

ToE introduces the idea that information has its own intrinsic temperature. This temperature does not measure heat. It measures how quickly the informational field changes.

When the informational field changes rapidly, geometry becomes “hot”—dynamic, curved, and energetic. When the field changes slowly, geometry becomes “cold”—smooth and stable.

This leads to a unifying principle: quantum behavior and geometric behavior are two sides of the same informational process.

1.3 Goals and Structure of the Paper

This work aims to establish the conceptual and mathematical foundations of ToE. It introduces the temperature of information, develops an informational uncertainty principle, constructs an informational action, and derives a field equation that generalizes Einstein’s equation.

The later sections explore how classical gravity, cosmology, and physical phenomena emerge from informational geometry.

1.4 Why the Temperature of Information Matters

If correct, ToE would unify quantum mechanics, thermodynamics, and gravity by showing that all three arise from the same informational substrate. It suggests that the constants of nature are not independent—they are expressions of one underlying informational process.

In this view, the universe is a thermodynamic hologram of an informational continuum.

2. Temperature as a Property of Information and Geometry

In everyday physics, temperature is tied to matter. It measures how fast particles move, how much energy they share, and how chaotic their motion becomes. But in the Theory of Entropicity (ToE), temperature takes on a deeper meaning. It becomes a property of the informational structure of the universe itself.

If information is the true foundation of physical reality, then temperature must describe how actively that information is changing. Instead of measuring molecular agitation, temperature becomes a measure of informational agitation — the intensity with which the informational field reorganizes.

In this framework, regions where information changes rapidly behave like “hot” zones. Their geometry is dynamic, curved, and responsive. Regions where information changes slowly behave like “cold” zones, where geometry is smooth, stable, and nearly static.

This leads to a profound equivalence: the temperature of information and the temperature of geometry are two sides of the same phenomenon. When information becomes more active, geometry becomes more dynamic. When information settles, geometry cools and smooths out.

In ToE, temperature is not something matter possesses. It is something information does.

3. Relation to Landauer’s Principle

Landauer’s Principle is one of the most important links between information and physics. It states that erasing information requires energy. In other words, information is physical — it cannot be changed or destroyed without a cost.

ToE takes this idea much further.

Instead of treating information as something that merely influences physical systems, ToE treats information as the system itself. The temperature of information becomes a universal property of the informational field, not just a measure of energy dissipation in computation.

Where Landauer describes the cost of erasing information, ToE describes the geometric consequences of possessing it.

In this view, energy, entropy, and geometry are inseparable. They are all expressions of how information flows. Landauer’s insight becomes a local manifestation of a deeper principle: the universe is driven by the irreversible flow of information, and temperature is the measure of that flow.

4. Understanding the Temperature of Information

In traditional physics, we don’t talk about information having a temperature. Temperature is something matter has. But ToE reframes this idea by asking a simple question: what does temperature really measure?

Temperature measures how quickly energy changes when entropy changes. Since entropy is fundamentally an informational quantity, temperature already has an informational meaning built into it.

ToE simply makes this explicit.

The temperature of information describes how rapidly the informational structure of the universe reorganizes. It is not about heat. It is about activity — the pace at which information reshapes its own geometry.

This makes the concept surprisingly natural. Information theory and thermodynamics already mirror each other. Entropy measures uncertainty in both. Free energy measures usable information. Temperature measures responsiveness.

ToE extends this parallel by giving information its own intrinsic temperature — a measure of how energetically it evolves.

4.1 What Temperature Really Measures

Temperature is often described as “how hot something is,” but at its core, it measures how sensitive energy is to changes in entropy. It is a measure of responsiveness. When entropy increases, temperature tells us how much energy must change in response.

Since entropy is an informational quantity, temperature already has an informational interpretation. ToE simply shifts the focus from matter to information itself.

4.2 The Step Taken by ToE

ToE proposes that wherever information is being reorganized, there is a flow of entropy. And wherever entropy flows, there is a temperature associated with that flow.

This temperature does not describe heat. It describes informational activity.

The temperature of information is the rate at which the informational field changes. It is the intensity of informational motion. And because geometry emerges from information, this temperature naturally becomes the temperature of geometry as well.

4.3 Why This Is Conceptually Natural

Thermodynamics and information theory have been intertwined for decades. They share the same mathematical structures. They describe the same kinds of uncertainty and organization.

If entropy and information are the same quantity, then temperature — which measures how systems respond to entropy — should also have an informational meaning.

In ToE, the temperature of information measures how rapidly the informational field reorganizes. When information changes quickly, geometry becomes more dynamic. When information changes slowly, geometry becomes more stable.

This is why ToE speaks of a “temperature of geometry.” Geometry is simply the visible expression of informational activity.

4.4 How It Differs from Ordinary Temperature

The temperature of information is not heat. It is not kinetic agitation. It is not something you can feel with your hand.

Instead, it is a field property that describes how energetically information reshapes its own geometry.

Ordinary temperature measures the motion of particles. Informational temperature measures the motion of information.

This distinction is subtle but transformative. It shifts temperature from being a property of matter to being a property of the universe’s informational foundation.

4.5 Why This Concept Is New

No existing physical theory assigns temperature to information itself. Thermodynamics ties temperature to energy. Information theory treats information as abstract. Even modern theories of gravity that use entropy still tie temperature to energy flow, not informational flow.

ToE is the first framework to propose that information itself has temperature — and that geometry inherits this temperature because it emerges from information.

This is a conceptual leap, but one that follows naturally from decades of hints in thermodynamics, quantum theory, and gravitational physics.

4.6 Summary: What the Temperature of Information Really Means

The temperature of information is not a metaphor. It is a measure of how rapidly information changes its own geometry. It is the pulse of the informational universe.

In ToE, temperature is not what matter feels. It is what information does.

The universe is constantly reorganizing itself, computing its own structure. The temperature of information measures how energetically that computation unfolds.

5. The Kinetic Analogy: Why Information Has a Temperature

In classical physics, temperature is tied to motion. When molecules move quickly, the temperature is high. When they move slowly, the temperature is low. This idea is so deeply embedded in our thinking that it’s easy to forget what temperature really represents: the average intensity of microscopic activity.

The Theory of Entropicity (ToE) extends this idea to information itself.

If information is a dynamic field — something that can change, propagate, oscillate, and reorganize — then it must also have a measure of how energetically it behaves. In ToE, the informational field is not static. It fluctuates, spreads, and reshapes itself across the fabric of reality. These fluctuations are not random; they define the structure of geometry and the behavior of physical systems.

The temperature of information is the measure of this activity. When the informational field fluctuates rapidly, the temperature is high. When it changes slowly, the temperature is low. This mirrors the kinetic interpretation of temperature in ordinary physics, but applied to the deeper substrate of information rather than matter.

In this sense, the universe is constantly “computing” its own structure, and the temperature of information tells us how energetically that computation is taking place.

6. How the Temperature of Information Could Be Measured

Although the temperature of information is introduced as a theoretical concept, it is not beyond the reach of measurement. Just as ordinary temperature can be inferred from the behavior of particles, the temperature of information can be inferred from the behavior of systems where information and entropy play a central role.

Several physical contexts offer clues:

Quantum information systems

In quantum computers and simulators, entanglement spreads through a system in measurable ways. The rate at which this entanglement grows can serve as a proxy for informational temperature. Faster growth means a “hotter” informational environment.

Black hole physics

Black holes provide one of the clearest windows into the relationship between entropy and geometry. Their temperature and entropy are directly tied to the structure of spacetime. In ToE, these quantities reflect the temperature of the underlying informational field.

Cosmology

The universe as a whole evolves through massive changes in entropy. As the cosmos expands and cools, its informational geometry changes as well. Large‑scale entropy production can be interpreted as a shift in the temperature of information across cosmic history.

These examples show that the temperature of information is not an abstract idea. It is a measurable feature of systems where information, entropy, and geometry interact. We may not yet have a direct “informational thermometer,” but the physical world already provides indirect ways to observe the phenomenon.

7. Why the Temperature of Information Is a New Concept

The idea that information has temperature is not found in traditional physics. Historically, temperature has always been tied to matter — to particles, energy, and heat. Even when entropy entered the world of information theory, temperature remained firmly rooted in thermodynamics.

Only recently have theories of gravity and spacetime begun to treat geometry as a thermodynamic system. But even in these approaches, temperature is still tied to energy flow, not informational flow.

The Theory of Entropicity (ToE) takes the next step. It proposes that information itself is a physical field with its own dynamics. Once information is treated as something that moves, interacts, and evolves, it naturally acquires a temperature. This temperature is not metaphorical. It is the thermodynamic descriptor of informational activity.

This is why the temperature of information is a genuinely new insight. It emerges only when information is elevated from a descriptive tool to the fundamental substance of reality.

8. Why the Temperature of Information Matters

Throughout the history of physics, temperature has been tied to matter. It measures how particles move and how energy is distributed. But as our understanding of entropy deepened, it became clear that entropy is not just a property of matter — it is a property of information.

Shannon showed that entropy measures uncertainty. Jaynes showed that statistical mechanics can be derived from principles of information inference. Black hole physics revealed that geometry itself carries entropy and temperature. Modern theories of gravity suggest that spacetime may be a thermodynamic system.

ToE brings all these threads together.

If information is the foundation of reality, then temperature must describe the activity of information itself. The temperature of information becomes the missing link that unifies thermodynamics, quantum mechanics, and geometry.

In this view:

Temperature measures how energetically information reorganizes.
Geometry is the visible expression of informational activity.
The universe evolves through the flow of information, not the motion of matter.

The temperature of information is the pulse of the informational universe — the rate at which reality computes itself.

App Deployment on the Theory of Entropicity (ToE):

App on the Theory of Entropicity (ToE): Click or Open on web browser (a GitHub Deployment - WIP): Theory of Entropicity (ToE)

https://phjob7.github.io/JOO_1PUBLIC/index.html

Sources — help

References

Obidi, John Onimisi (30th December, 2025). From the Temperature of Information to the Temperature of Geometry: The Foundations of the Theory of Entropicity (ToE) and the Unification of Quantum and Entropic Reality - A Unified Framework for the Thermodynamic, Quantum, and Geometric Foundations of Physical Reality. Figshare. https://doi.org/10.6084/m9.figshare.30976342
Obidi, John Onimisi (27th December, 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.30958670
Obidi, John Onimisi. (12th 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
John Onimisi Obidi. (6th November, 2025). Comparative analysis between john onimisi obidi’s theory of entropicity (toe) and waldemar marek feldt’s feldt–higgs universal bridge (f–hub) theory. International Journal of Current Science Research and Review, 8(11), pp. 5642–5657, 19th November 2025. URL: https://doi.org/10.47191/ijcsrr/V8-i11–21
Obidi, John Onimisi. 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
Obidi, John Onimisi (17th October 2025). On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics. Figshare. https://doi.org/10.6084/m9.figshare.30337396.v2
Obidi, John Onimisi. 2025. A Simple Explanation of the Unifying Mathematical Architecture of the Theory of Entropicity (ToE): Crucial Elements of ToE as a Field Theory. Cambridge University. Published October 20, 2025. https://doi.org/10.33774/coe-2025-bpvf3
Obidi, John Onimisi (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
Obidi, John Onimisi. Unified Field Architecture of Theory of Entropicity (ToE). Encyclopedia. Available online: https://encyclopedia.pub/entry/59276 (accessed on 19 November 2025).
Obidi, John Onimisi. (4 November, 2025). The Theory of Entropicity (ToE) Derives Einstein’s Relativistic Speed of Light © as a Function of the Entropic Field: ToE Applies Logical Entropic Concepts and Principles to Derive Einstein’s Second Postulate. Cambridge University. https://doi.org/10.33774/coe-2025-f5qw8-v2
Obidi, John Onimisi. (28 October, 2025). The Theory of Entropicity (ToE) Derives and Explains Mass Increase, Time Dilation and Length Contraction in Einstein’s Theory of Relativity (ToR): ToE Applies Logical Entropic Concepts and Principles to Verify Einstein’s Relativity. Cambridge University. https://doi.org/10.33774/coe-2025-6wrkm
HandWiki contributors, “Physics:Theory of Entropicity (ToE) Derives Einstein’s Special Relativity,” HandWiki, https://handwiki.org/wiki/index.php?title=Physics:Theory_of_Entropicity_(ToE)_Derives_Einstein%27s_Special_Relativity&oldid=3845936

Further Resources on the Theory of Entropicity (ToE):

Website: Theory of Entropicity ToE — https://theoryofentropicity.blogspot.com
LinkedIn: Theory of Entropicity ToE — https://www.linkedin.com/company/theory-of-entropicity-toe/about/?viewAsMember=true
Notion-1: Theory of Entropicity (ToE)
Notion-2: Theory of Entropicity (ToE)
Notion-3: Theory of Entropicity (ToE)
Notion-4: Theory of Entropicity (ToE)
Substack: Theory of Entropicity (ToE) — John Onimisi Obidi | Substack
Medium: Theory of Entropicity (ToE) — John Onimisi Obidi — Medium
SciProfiles: Theory of Entropicity (ToE) — John Onimisi Obidi | Author
Encyclopedia.pub: Theory of Entropicity (ToE) — John Onimisi Obidi | Author
HandWiki contributors, “Biography: John Onimisi Obidi,” HandWiki, https://handwiki.org/wiki/index.php?title=Biography:John_Onimisi_Obidi&oldid=2743427 (accessed October 31, 2025).
HandWiki Contributions: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki
HandWiki Home: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki
HandWiki Homepage-User Page: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki
Academia: Theory of Entropicity (ToE) — John Onimisi Obidi | Academia
ResearchGate: Theory of Entropicity (ToE) — John Onimisi Obidi | ResearchGate
Figshare: Theory of Entropicity (ToE) — John Onimisi Obidi | Figshare
Authoria: Theory of Entropicity (ToE) — John Onimisi Obidi | Authorea
Social Science Research Network (SSRN): Theory of Entropicity (ToE) — John Onimisi Obidi | SSRN
Wikidata contributors, Biography: John Onimisi Obidi “Q136673971,” Wikidata, https://www.wikidata.org/w/index.php?title=Q136673971&oldid=2423782576 (accessed November 13, 2025).
Google Scholar: ‪John Onimisi Obidi — ‪Google Scholar
IJCSRR: International Journal of Current Science Research and Review - Theory of Entropicity (ToE) - John Onimisi Obidi | IJCSRR
Cambridge University Open Engage (CoE): Collected Papers on the Theory of Entropicity (ToE)

Theory of Entropicity (ToE) by John Onimisi Obidi

Wikipedia

Tuesday, 30 December 2025