The Theory of Entropicity (ToE) Goes Beyond Holographic Pseudo-Entropy: From Boundary Diagnostics to a Universal Entropic Field Theory

The Theory of Entropicity (ToE) Goes Beyond Holographic Pseudo-Entropy: From Boundary Diagnostics to a Universal Entropic Field Theory

                               The Obidi Action of the Theory of Entropicity (ToE)

This paper presents a systematic comparison between the recently developed pseudo entropy framework of Takayanagi, Kusuki, and Tamaoka and the Theory of Entropicity (ToE). While pseudo–entropy has revealed a remarkable boundary route to the linearized Einstein equation in dS3, the Theory of Entropicity proposes a far more fundamental idea: that entropy is not a boundary diagnostic of geometry, but the underlying field from which geometry, matter, motion, and time themselves emerge. The discussion that follows demonstrates how the pseudo–entropy program fits naturally within the broader structure of ToE, and how the ToE framework generalizes, extends, and ultimately surpasses it. The pseudo–entropy construction shows that a non–Hermitian generalization of entanglement entropy in a two–dimensional CFT satisfies a first law whose bulk dual reproduces the perturbative Einstein equation in dS3. Moreover, infinitesimal variations of pseudo–entropy obey a Klein–Gordon equation on a kinematic dS2 space, suggesting the emergence of time from Euclidean CFT data. In this paper, we reinterpret these results within the Theory of Entropicity by showing that the same Klein–Gordon structure appears as the boundary–projected, linearized limit of the Master Entropic Equation derived from the Local Obidi Action. Thus, what pseudo–entropy identifies kinematically from the boundary, ToE generates dynamically in the bulk through the entropic field S(x). The manuscript further embeds pseudo–entropy into a broader landscape of entropic approaches — Jacobson’s thermodynamic derivation of Einstein equations, Padmanabhan’s emergent spacetime, Ver linde’s entropic gravity, Caticha’s entropic inference, and Bianconi’s metric relative entropy. Where these earlier programs emphasize information, thermodynamics, or emergence, ToE provides a uni fying ontological principle: entropy itself is the fundamental field of the universe. By promoting the modular–like operator ∆ to a dynamical object through the Spectral Obidi Action, ToE offers a natural explanation of dark matter, dark energy, and vacuum entropic pressure — domains entirely absent from the pseudo–entropy framework. This paper shows explicitly how Bianconi’s relative–entropy action and the Takayanagi–Kusuki–Tamaoka pseudo–entropy construction both appear as limiting cases of the Obidi Actions. Finally, we demonstrate that ToE provides a unified entropic–spectral variational principle in which bosons and fermions arise from the same foundational structure. The spectral interpretation of bosonic actions, the Dirac–based fermionic bilinears, and geometric actions such as Einstein–Hilbert and Yang–Mills all emerge as projections of the Local and Spectral Obidi Actions. This paper therefore positions pseudo–entropy not as an alternative to ToE, but as a special holographic shadow of a deeper entropic field theory. In this sense, the present work does not merely compare two independent approaches. Rather, it establishes a hierarchical synthesis: pseudo–entropy reconstructs gravity from boundary information, while the Theory of Entropicity constructs gravity, geometry, quantum structure, and temporal dynam ics from an underlying entropic field. This manuscript argues that pseudo–entropy is best understood not as a standalone gravitational principle, but as a boundary manifestation of the universal entropic dynamics formulated by the Theory of Entropicity (ToE).

Abstract

The recent work of Takayanagi, Kusuki, and Tamaoka has introduced the concept of holographic pseudo-entropy in non-unitary CFT2 and demonstrated a striking equivalence: the first law of pseudo entropy is precisely dual to the linearized Einstein equation in three-dimensional de Sitter space (dS3) once one allows complexified extremal surfaces in the bulk. Moreover, variations of pseudo-entropy obey a Klein–Gordon equation on the kinematical space dS2, offering an emergent time structure arising from an Euclidean boundary theory. In this paper we show that while the holographic pseudo-entropy program represents an important boundary diagnostic of gravitational dynamics, it remains a restricted kinematical construction tied to holography, non-unitary conformal field theories, and perturbative de Sitter gravity. By contrast, the Theory of Entropicity (ToE) treats entropy S(x) as the fundamental physical field of nature, endowed with a local variational principle (the Local Obidi Action) and a spectral variational principle (the Spectral Obidi Action). From these actions one derives the Master Entropic Equation, entropic geodesics, irreversible dynamics, and a unified description of gravity, time, quantum processes, and information geometry. The goal of this work is threefold. First, we present a precise and self-contained exposition of the Takayanagi–Kusuki–Tamaoka framework. Second, we develop the Theory of Entropicity as a universal entropic field theory whose dynamics extend far beyond the holographic pseudo-entropy correspondence. Third, we provide a systematic comparison showing how ToE absorbs pseudo-entropy as a special boundary manifestation of a deeper entropic field, thereby revealing why pseudo-entropy reproduces only the linearized sector of gravitational physics while ToE yields a fully nonlinear, time-asymmetric, and information-geometric unification of physical law.

Keywords

Amari–Čencov α–Connections; Araki Relative Entropy; Atiyah–Singer Index Theorem;

Bekenstein–Hawking Entropy; Bosons; Canonical Quantization; Complex Geodesics; Dark Matter; Dark

Energy; dS/CFT Correspondence; Dirac–Kähler Fermions; Dirac Spinors; Einstein–Hilbert Action; Emer

gent Geometry; Entropic Field; Entropic Geodesics; Entropy Geometry; Entropy as Ontic Field; Fermions;

Fisher–Rao Metric; Fubini–Study Metric; G-Field (Bianconi); Ginestra Bianconi; Holographic Pseudo

Entropy; Information Geometry; Jacobson Thermodynamics; Kinematic Space (dS2); Klein–Gordon

Equation (Pseudo-Entropy); Local Obidi Action (LOA); Master Entropic Equation (MEE); Modular Op

erator ∆; Nonlinear Entropic Dynamics; Obidi Actions; Padmanabhan Entropic Gravity; Pseudo-Entropy

(Takayanagi–Kusuki–Tamaoka); Quantum Entanglement; Quantum Gravity; Rényi Entropy; Relative

Entropy; Shannon Information; Small Positive Cosmological Constant; Spectral Action; Spectral Dynam

ics; Spectral Geometry; Spectral Obidi Action (SOA); Spectral Theories; Takayanagi–Kusuki–Tamaoka

Pseudo-Entropy; Theory of Entropicity (ToE); Thermodynamic Gravity; Tsallis Entropy; Vuli–Ndlela

Integral; Yang–Mills Theory.

References

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

Further Resources on the Theory of Entropicity (ToE):

1. Website: Theory of Entropicity ToE —

https://theoryofentropicity.blogspot.com

2. LinkedIn: Theory of Entropicity ToE — https://www.linkedin.com/company/theory-of-entropicity-toe/about/?viewAsMember=true

3. Notion: Theory of Entropicity (ToE)

4. Substack: Theory of Entropicity (ToE) — John Onimisi Obidi | Substack

5. Medium: Theory of Entropicity (ToE) — John Onimisi Obidi — Medium

6. SciProfiles: Theory of Entropicity (ToE) — John Onimisi Obidi | Author

7. Encyclopedia.pub: Theory of Entropicity (ToE) — John Onimisi Obidi | Author

8. HandWiki contributors, “Biography: John Onimisi Obidi,” HandWiki, https://handwiki.org/wiki/index.php?title=Biography:John_Onimisi_Obidi&oldid=2743427 (accessed October 31, 2025).

9. HandWiki Contributions: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki

10. HandWiki Home: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki

11. HandWiki Homepage-User Page: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki

12. Academia: Theory of Entropicity (ToE) — John Onimisi Obidi | Academia

13. ResearchGate: Theory of Entropicity (ToE) — John Onimisi Obidi | ResearchGate

14. Figshare: Theory of Entropicity (ToE) — John Onimisi Obidi | Figshare

15. Authoria: Theory of Entropicity (ToE) — John Onimisi Obidi | Authorea

16. Social Science Research Network (SSRN): Theory of Entropicity (ToE) — John Onimisi Obidi | SSRN

17. Wikidata contributors, Biography: John Onimisi Obidi “Q136673971,” Wikidata, https://www.wikidata.org/w/index.php?title=Q136673971&oldid=2423782576 (accessed November 13, 2025).

18. Google Scholar: ‪John Onimisi Obidi — ‪Google Scholar

19. Cambridge University Open Engage (CoE): Collected Papers on the Theory of Entropicity (ToE)

On the Union of Ginestra Bianconi and John Onimisi Obidi: Progress of the Theory of Entropicity (ToE) as a Field Theory in Theoretical and Mathematical Physics

On the Union of Ginestra Bianconi and John Onimisi Obidi: Progress of the Theory of Entropicity (ToE) as a Field Theory in Theoretical and Mathematical Physics

                     The Obidi Action of the Theory of Entropicity (ToE)

The evolution of theoretical physics has often been marked by unexpected unions — moments when distinct intellectual traditions converge to produce new frameworks of understanding. The collaboration between Ginestra Bianconi, known for her pioneering work in network theory and statistical mechanics, and John Onimisi Obidi, whose contributions to entropic formulations and mathematical physics have been steadily gaining recognition, represents one such union. Their combined perspectives have given rise to a more formal articulation of the Theory of Entropicity (ToE), positioning it as a candidate for a field theory in theoretical and mathematical physics.

                            The Obidi Action of the Theory of Entropicity (ToE)

Entropicity as a Conceptual Foundation

Entropy has long been a cornerstone of physics, from thermodynamics to information theory. Yet, the notion of entropicity extends beyond entropy as a measure of disorder. It suggests a principle of generative structure, where systems evolve not merely toward equilibrium but toward complex configurations that balance order and randomness.

Bianconi’s work on multilayer networks and phase transitions provides the mathematical scaffolding for this idea, while Obidi’s formulations emphasize entropicity as a field property — a quantity that can be distributed, conserved, and transformed across domains of physics.

Toward a Field Theory of ToE

The ambition of ToE is not simply to describe entropy but to elevate entropicity into a unifying field. This involves:

• Defining entropicity as a tensorial field, capable of interacting with matter and energy.
• Exploring its role in phase transitions, where entropicity mediates between microstates and macrostates.
• Extending its reach into quantum information, where entropicity may serve as a bridge between classical thermodynamics and quantum coherence.

Such a formulation aligns with the broader tradition of field theories in physics, from electromagnetism to quantum chromodynamics, but introduces a novel axis: the dynamics of complexity itself.

Implications for Theoretical and Mathematical Physics

The union of Bianconi and Obidi’s approaches suggests several promising directions:

• Network Cosmology: Viewing the universe as a multilayer network, where entropicity governs connectivity and evolution.
• Information Geometry: Embedding entropicity within geometric frameworks, linking statistical manifolds to physical fields.
• Complex Systems Physics: Providing a rigorous field-theoretic language for phenomena ranging from biological evolution to social dynamics.

In each case, entropicity functions not as a metaphor but as a quantifiable field variable, opening pathways for predictive modeling and experimental validation.

Conclusion: A New Horizon

The Theory of Entropicity, as advanced through the union of Bianconi and Obidi’s insights, represents a bold step toward reconceptualizing entropy not as a passive measure but as an active field of physics. If successful, ToE could unify disparate domains — thermodynamics, information theory, quantum mechanics — under a single entropic framework.

For theoretical and mathematical physics, this is more than an incremental advance; it is a reorientation toward complexity as a fundamental property of nature.

References

Obidi, John Onimisi (12 Nov. 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). Figshare. https://doi.org/10.6084/m9.figshare.30596129.v1

Further Resources on the Theory of Entropicity (ToE):

1. Website: Theory of Entropicity ToE —

https://theoryofentropicity.blogspot.com

2. LinkedIn: Theory of Entropicity ToE — https://www.linkedin.com/company/theory-of-entropicity-toe/about/?viewAsMember=true

3. Notion: Theory of Entropicity (ToE)

4. Substack: Theory of Entropicity (ToE) — John Onimisi Obidi | Substack

5. Medium: Theory of Entropicity (ToE) — John Onimisi Obidi — Medium

6. SciProfiles: Theory of Entropicity (ToE) — John Onimisi Obidi | Author

7. Encyclopedia.pub: Theory of Entropicity (ToE) — John Onimisi Obidi | Author

8. HandWiki contributors, “Biography: John Onimisi Obidi,” HandWiki, https://handwiki.org/wiki/index.php?title=Biography:John_Onimisi_Obidi&oldid=2743427 (accessed October 31, 2025).

9. HandWiki Contributions: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki

10. HandWiki Home: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki

11. HandWiki Homepage-User Page: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki

12. Academia: Theory of Entropicity (ToE) — John Onimisi Obidi | Academia

13. ResearchGate: Theory of Entropicity (ToE) — John Onimisi Obidi | ResearchGate

14. Figshare: Theory of Entropicity (ToE) — John Onimisi Obidi | Figshare

15. Authoria: Theory of Entropicity (ToE) — John Onimisi Obidi | Authorea

16. Social Science Research Network (SSRN): Theory of Entropicity (ToE) — John Onimisi Obidi | SSRN

17. Wikidata contributors, Biography: John Onimisi Obidi “Q136673971,” Wikidata, https://www.wikidata.org/w/index.php?title=Q136673971&oldid=2423782576 (accessed November 13, 2025).

18. Google Scholar: ‪John Onimisi Obidi — ‪Google Scholar

19. Cambridge University Open Engage (CoE): Collected Papers on the Theory of Entropicity (ToE) 

The Theory of Entropicity (ToE) Explains the Constancy of the Speed of Light c in Albert Einstein’s Theory of Relativity (ToR): The Entropic Origin of the Speed of Light c from the Theory of Entropicity (ToE)

The Theory of Entropicity (ToE) Explains the Constancy of the Speed of Light c in Albert Einstein’s Theory of Relativity (ToR)

The Entropic Origin of the Speed of Light c from the Theory of Entropicity (ToE)

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The Obidi Action of the Theory of Entropicity (ToE)

The Theory of Entropicity (ToE) Explains Why the Speed of Light c is a Constant in Einstein’s Theory of Relativity (ToR)

We have previously dwelt on how the Theory of Entropicity (ToE) explains why the speed of light is a constant (c) according to Einstein’s beautiful and revolutionary Theory of Relativity (ToR). Here, we dive deeper into giving the core mechanism for this action in the Theory of Entropicity (ToE) [first formulated by John Onimisi Obidi — Researcher, Investigator, Thinker, Physicist, Philosopher, and Humanist — different from the unrelated social media personality of a similar name] that explains Einstein’s constancy of the speed of light in his Theory of Relativity (ToR) - that is, we are providing a deeper version of ToE’s explanation of the "why" behind the "what."

Further Exploratory and Revolutionary Insights of the Theory of Entropicity (ToE) Into Explaining the Constancy of the Speed of Light (c) in Einstein’s Theory of Relativity (ToR).

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Table of Contents

1. What "You Are Made of the Field" Actually Means
Let's use a better analogy than a movie screen which we have used elsewhere:[1] A whirlpool in a river.

The River: This represents the fundamental Entropic Field. It has an intrinsic property: the maximum speed its current can flow.

The Whirlpool: This represents a stable object—a particle, a clock, an observer. A whirlpool is not a separate "thing" floating in the water; it is a stable, organized pattern of the water itself. Its existence is defined by its structure and its interaction with the surrounding flow.

When we say "you are made of the field,"[1] it means you (and your clock and ruler) are like that whirlpool. You are not an independent entity moving through a passive, empty space. You are a complex, stable pattern of activity within the universe's fundamental entropic field.

Your physical being, the forces holding your atoms together, and the regular processes inside your clock are all manifestations of the rules of this field. Therefore, your properties are not absolute; they are relational and dependent on your interaction with the rest of the field (the river).

2. The ToE Mechanism for Time Dilation and Length Contraction
To explain why time slows and length contracts, we must use the core principles of ToE, which are all based on entropy.

Here is the proposed mechanism, step-by-step.

The Foundational Principle: Existence is a Battle Against Entropy
According to ToE (and standard physics), any organized system—a clock, a ruler, a living cell—is a low-entropy state. To exist, it must constantly work to maintain its structure and order against the universe's natural tendency to dissolve into chaos (the Second Law of Thermodynamics). It does this by processing information and managing entropy flow. Think of it as having an "entropic budget"[2][3][4][5][6] just to remain stable and functional.

Step 1: Explaining Time Dilation (Why Clocks Slow Down)
What is a Clock? A clock is a system designed to perform a highly regular, repeating internal process (a "tick"). This tick could be the swing of a pendulum, the vibration of a crystal, or the transition of a cesium atom.

The "Entropic Cost" of Ticking: For this tick to be regular, the clock must use part of its "entropic budget" to ensure the process repeats identically, fighting off microscopic disorder. This is its normal operating cost while stationary.

The "Entropic Cost" of Motion: According to ToE, "motion" is not passive. Moving through the entropic field means a system is constantly interacting with new regions of the field. This creates an additional and continuous entropic "load" or "stress" on the system. It's like a swimmer not only having to manage their own body heat and energy (internal entropy) but also having to fight the current and drag of the water (external entropic interaction).

The Result of the Theory of Entropicity (ToE): Reallocation of the Budget. The clock still has the same fundamental priority: it must maintain its structural integrity. Faced with this new external entropic load from motion, it must divert resources from its "entropic budget" to deal with it. The work of simply staying intact in the face of this motion takes precedence. Consequently, there is less "budget" available for its primary function—the regular "ticking."

Conclusion of the Theory of Entropicity (ToE): The internal process of the clock—its tick—is forced to run slower. Time dilation is the observable consequence of a system prioritizing its structural integrity over its internal functions when under the entropic stress of motion. Ordinarily, this is not obvious and not readily observable; but it becomes crucial as the speed increases; as the speed increases, it reaches a limit at which it wants to cross the entropic bound, then it is halted, because it cannot go faster than entropy! This is the No-Rush Theorem and also why Einstein's Relativity of the speed of light is constant and why it is the maximum speed of all propagations.

Entropy thus ensures that no interaction can occur faster or slower than Entropy allows, and no propagation can go faster than Entropy permits. This is ToE's No-Rush Theorem[7] in its most encompassing and celebrated form. Thus, Entropy is what actually dictates how fast or slow any motion should be. This conclusion is only natural, unavoidable and inescapable, because since Entropy is what dictates and constrains motion according to the Theory of Entropicity (ToE), then the same Entropy must constrain the speed of motion itself; that is, how fast or slow interactions and propagations and objects can move in the Entropic Field itself.

Step 2: Explaining Length Contraction (Why Rulers Shrink)
What is a Ruler? A ruler is a rigid object. Its length is a stable property defined by the equilibrium distance between its atoms. This equilibrium is a delicate balance of electromagnetic forces, which ToE recasts as constraints within the entropic field.

The "Entropic Headwind": When the ruler moves, it experiences the same entropic stress, but this time it's directional. The front of the ruler is continuously interacting with "new" parts of the field before the back does. This creates a kind of "entropic pressure" or "headwind" that pushes against the front of the ruler.

The Result: A New Equilibrium. The system (the ruler) must find a new stable state to cope with this constant directional pressure. The internal forces readjust to a new, slightly compressed equilibrium in the direction of motion. The atoms are pushed closer together until their repulsive forces are strong enough to balance the new external "entropic headwind."

Conclusion: The ruler physically becomes shorter in its direction of motion. Length contraction is the physical deformation of an object as it re-establishes structural equilibrium under the directional entropic pressure of moving through the field.

Table

This explanation attempts to ground the strange effects of relativity in a physical, causal mechanism rooted in entropy management, rather than leaving them as abstract geometric consequences of a postulate. It is a bold and unproven claim, but it is the kind of deeper explanation that the Theory of Entropicity aims to provide.

References

Obidi, John Onimisi. The Theory of Entropicity (ToE) Simply Explained Qualitatively. Encyclopedia. Available online: https://encyclopedia.pub/entry/58652 (accessed on 20 July 2025).
Obidi, John Onimisi. A Critical Review of the Theory of Entropicity (ToE) on Original Contributions, Conceptual Innovations, and Pathways towards Enhanced Mathematical Rigor: An Addendum to the Discovery of New Laws of Conservation and Uncertainty. Cambridge University; 30 June 2025. https://doi.org/10.33774/coe-2025-hmk6n
Obidi, John Onimisi. Einstein and Bohr Finally Reconciled on Quantum Theory: The Theory of Entropicity (ToE) as the Unifying Resolution to the Problem of Quantum Measurement and Wave Function Collapse. Cambridge University; 14 April 2025. https://doi.org/10.33774/coe-2025-vrfrx
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Speed of Light from Theory of Entropicity (ToE)
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This review takes an open-minded stance towards John Onimisi Obidi’s “Derivation of Speed of Light (c) from the Theory of Entropicity (ToE),” assessing its intellectual ambition and methodological clarity rather than its publication status. It highlights the bold goal of explaining why c has its specific value and why it’s invariant, by unifying inputs from general relativity (G), quantum mechanics (ℏ), and thermodynamics/information theory (Boltzmann constant kB and entropy S). A key strength is the paper’s familiar, step-by-step theoretical structure: it posits a master entropic action, derives nonlinear field equations via least action, linearizes around a background to study small disturbances, identifies the characteristic propagation speed of “entropic waves,” and constructs an “Entropic Lorentz Group (ELG)” to argue for observer-independent c. This rigorous framework makes the proposal coherent and formally sound. The review also applauds the creative, heuristic value of promoting entropy to a dynamical field, and introducing “entropic stiffness” and “entropic inertia.” These concepts offer an intuitive picture in which the ratio of stiffness to inertia—fixed by fundamental constants—naturally yields c. The suggestion that c emerges from a balance of gravitational, quantum, and thermal forces is framed as an elegant, potentially deep origin for the constant. Importantly, the paper outlines avenues for constructive development: incorporating irreversibility and Fisher information to deepen the model, and exploring testable predictions, such as deviations in c under extreme entropy gradients (e.g., near black holes). Such possibilities move the theory toward falsifiability. In conclusion, while speculative, the work serves as a provocative conceptual catalyst, encouraging physicists to reconsider entropy’s possible dynamical role and potentially guiding future breakthroughs.

Prospects of The Evolving Theory of Entropicity (ToE)
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The Theory of Entropicity (ToE) presents an ambitious and intriguing alternative to current fundamental physics theories, particularly General Relativity and Quantum Field Theory. Its prospects depend heavily on its ability to withstand rigorous scrutiny, make verifiable predictions, and gain acceptance within the broader scientific community.

Entropic Cost of Motion in Theory of Entropicity(ToE)
Entry
In the Theory of Entropicity (ToE), the “entropic cost of motion” is the extra entropy a system must overcome or redistribute to move or change state within the universe’s entropy field. Unlike classical inertia, this cost arises from field-theoretic constraints embedded in spacetime, growing with velocity, energy, and informational complexity. Motion disturbs the surrounding entropy field and, under the No-Rush Theorem, can’t propagate changes faster than light. Accelerating reconfigures local entropy gradients, demanding work to realign field structures. As a system nears light speed, the entropic gradient steepens, making further acceleration prohibitively costly—hence massive objects can never reach c. Analogies liken the field to a viscous cosmic fluid or a series of toll gates where faster motion incurs higher “entropy drag.” Relativistic effects—time dilation and length contraction—emerge naturally as entropic field distortions: moving clocks slow because more entropy is committed to motion than internal processes, and lengths contract due to compressed entropy distributions. This reframes the invariant speed of light as the maximum rate of entropic rearrangement, offering a causal foundation for Einstein’s postulates. In weak, homogeneous fields, ToE reproduces standard relativistic kinematics while unifying thermodynamic irreversibility, quantum constraints, and relativistic motion. The Entropic Explanation of Relativity (EER) formalizes these effects as entropy field responses to motion-induced entropy redistribution, merging geometry and thermodynamics under one framework.

Theory of Entropicity (ToE): Path To Unification of Physics
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This paper presents the Theory of Entropicity (ToE) by John Onimisi Obidi, a groundbreaking framework that redefines entropy not as a byproduct of disorder, but as the fundamental field of existence—the dynamic fabric from which space, time, motion, information, and matter arise. Just as Einstein elevated the speed of light to a universal constant, ToE elevates entropy to a universal field that governs all physical processes.

Relativistic Time Dilation, Lorentz Contraction: Theory of Entropicity
Entry

In the Theory of Entropicity (ToE), first formulated and developed by John Onimisi Obidi, entropy is a dynamic universal field that governs both time’s arrow and motion’s limits, rather than merely quantifying disorder. This field imposes two core constraints: it drives all systems irreversibly toward higher entropy and enforces a maximum causal‐propagation rate—experienced as the speed of light, c. Rather than a geometric axiom, c emerges from the entropic field’s structure: massless signals follow paths of minimal entropic resistance set by local and global entropy configurations. Relativistic time dilation and length contraction arise as entropic‐field distortions. As an object nears c, rising entropy resistance slows its internal processes (time dilation) and compresses spatial intervals (length contraction). The entropic No-Rush Theorem forbids any superluminal interaction by preventing the field from establishing conditions faster than its propagation limit. Likewise, the finite speed of quantum entanglement or wave‐function collapse reflects the same entropic time constraint. In this framework, Einstein’s field equations appear as an emergent entropic geometry: spacetime curvature encodes how the entropy field constrains motion and interaction. Thus, ToE unifies thermodynamics, quantum mechanics, and relativity by revealing c as a thermodynamic consequence of entropy’s universal governance.

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References

Obidi, John Onimisi (12 Nov. 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). Figshare. https://doi.org/10.6084/m9.figshare.30596129.v1

Further Resources on the Theory of Entropicity (ToE):

1. Website: Theory of Entropicity ToE —  https://theoryofentropicity.blogspot.com

2. LinkedIn: Theory of Entropicity ToE —  https://www.linkedin.com/company/theory-of-entropicity-toe/about/?viewAsMember=true

3. Notion: Theory of Entropicity (ToE)

4. Substack: Theory of Entropicity (ToE) — John Onimisi Obidi | Substack

5. Medium: Theory of Entropicity (ToE) — John Onimisi Obidi — Medium

6. SciProfiles: Theory of Entropicity (ToE) — John Onimisi Obidi | Author

7. Encyclopedia.pub: Theory of Entropicity (ToE) — John Onimisi Obidi | Author

8. HandWiki contributors, “Biography: John Onimisi Obidi,” HandWiki, https://handwiki.org/wiki/index.php?title=Biography:John_Onimisi_Obidi&oldid=2743427 (accessed October 31, 2025).

9. HandWiki Contributions: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki

10. HandWiki Home: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki

11. HandWiki Homepage-User Page: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki

12. Academia: Theory of Entropicity (ToE) — John Onimisi Obidi | Academia

13. ResearchGate: Theory of Entropicity (ToE) — John Onimisi Obidi | ResearchGate

14. Figshare: Theory of Entropicity (ToE) — John Onimisi Obidi | Figshare

15. Authoria: Theory of Entropicity (ToE) — John Onimisi Obidi | Authorea

16. Social Science Research Network (SSRN): Theory of Entropicity (ToE) — John Onimisi Obidi | SSRN

17. Wikidata contributors, Biography: John Onimisi Obidi “Q136673971,” Wikidata, https://www.wikidata.org/w/index.php?title=Q136673971&oldid=2423782576 (accessed November 13, 2025).

18. Google Scholar: ‪John Onimisi Obidi — ‪Google Scholar

19. Cambridge University Open Engage (CoE): Collected Papers on the Theory of Entropicity (ToE)

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John Onimisi Obidi — Creator of the Theory of Entropicity (ToE): Bio

John Onimisi Obidi — Creator of the Theory of Entropicity (ToE)

Bio

Last updated: Friday, January 30, 2026

John Onimisi Obidi (who is a scientific researcher, investigator, thinker, physicist, consultant, philosopher, and humanist) is the originator and creator of the Theory of Entropicity (ToE), a foundational framework in modern physics that derives the speed of light, relativistic effects, and quantum constraints from the universal entropic field. His independent research redefines entropy not as a statistical abstraction but as a dynamic field governing time, causality, and motion. Through the Master Entropic Equation (MEE) and the Obidi Action, ToE unifies thermodynamics, relativity, and quantum mechanics by showing that Einstein’s postulates emerge as entropic inevitabilities. Obidi’s work emphasizes reproducible workflows, rigorous LaTeX documentation, and open publishing strategies to ensure both scholarly permanence and global outreach. He is committed to establishing keyword authority and domain visibility for the Theory of Entropicity (ToE) across platforms, making his research the definitive source for entropic field dynamics. Importantly, John Onimisi Obidi is a scientific researcher and the creator of ToE, distinct from the unrelated social media consultant of similar name. His mission is to build a lasting corpus of ToE research that bridges information geometry, entropy conservation, and spacetime physics, while remaining accessible to both technical and non‑technical audiences.

John Onimisi Obidi is a prominent theoretical physicist best known for his groundbreaking work on the Theory of Entropicity (ToE), which redefines the concept of entropy in physics.

Theory of Entropicity (ToE)

Obidi is best known for formulating the Theory of Entropicity (ToE), which he first developed in February 2025. This theory posits that entropy is not merely a measure of disorder but a fundamental, dynamic field that drives all physical processes. The ToE aims to unify various areas of physics, including thermodynamics, relativity, and quantum mechanics, by treating entropy as a real field that influences time, causality, and motion.

Key aspects of the Theory of Entropicity include:

• Dynamic Field: Obidi's theory elevates entropy to a continuous, dynamic field responsible for physical laws and interactions, suggesting that all forces emerge from the constraints on this entropic field.
• Master Entropic Equation (MEE): This equation serves as a foundational element of the ToE, integrating various physical principles and providing a framework for understanding complex phenomena.
• Unification of Physics: The ToE seeks to bridge the historical divide between randomness and determinism by positing entropy as a mediating force between stochastic processes and deterministic physical laws.
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Publications and Impact

Obidi has published numerous papers and articles discussing his theories and their implications for modern physics. His work has been recognized for its potential to explain a variety of natural phenomena and for its conceptual appeal in the scientific community.

In summary, John Onimisi Obidi is a significant figure in contemporary physics, particularly known for his innovative approach to understanding entropy and its role in the universe through the Theory of Entropicity. His contributions continue to influence discussions in theoretical physics and related fields.

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References

Obidi, John Onimisi (12 Nov. 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). Figshare. https://doi.org/10.6084/m9.figshare.30596129.v1

Further Resources on the Theory of Entropicity (ToE):

1. Website: Theory of Entropicity ToE — 

https://theoryofentropicity.blogspot.com

2. LinkedIn: Theory of Entropicity ToE — https://www.linkedin.com/company/theory-of-entropicity-toe/about/?viewAsMember=true

3. Notion: Theory of Entropicity (ToE)

4. Substack: Theory of Entropicity (ToE) — John Onimisi Obidi | Substack

5. Medium: Theory of Entropicity (ToE) — John Onimisi Obidi — Medium

6. SciProfiles: Theory of Entropicity (ToE) — John Onimisi Obidi | Author

7. Encyclopedia.pub: Theory of Entropicity (ToE) — John Onimisi Obidi | Author

8. HandWiki contributors, “Biography: John Onimisi Obidi,” HandWiki, https://handwiki.org/wiki/index.php?title=Biography:John_Onimisi_Obidi&oldid=2743427 (accessed October 31, 2025).

9. HandWiki Contributions: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki

10. HandWiki Home: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki

11. HandWiki Homepage-User Page: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki

12. Academia: Theory of Entropicity (ToE) — John Onimisi Obidi | Academia

13. ResearchGate: Theory of Entropicity (ToE) — John Onimisi Obidi | ResearchGate

14. Figshare: Theory of Entropicity (ToE) — John Onimisi Obidi | Figshare

15. Authoria: Theory of Entropicity (ToE) — John Onimisi Obidi | Authorea

16. Social Science Research Network (SSRN): Theory of Entropicity (ToE) — John Onimisi Obidi | SSRN

17. Wikidata contributors, Biography: John Onimisi Obidi “Q136673971,” Wikidata, https://www.wikidata.org/w/index.php?title=Q136673971&oldid=2423782576 (accessed November 13, 2025).

18. Google Scholar: ‪John Onimisi Obidi — ‪Google Scholar

19. Cambridge University Open Engage (CoE): Collected Papers on the Theory of Entropicity (ToE)