A Brief Explanation of the Kolmogorov-Obidi Correspondence (KOC) in the Theory of Entropicity (ToE): From Algorithmic Information Complexity to the Entropic Theory of Fields 

In the Theory of Entropicity (ToE), the Kolmogorov–Obidi Correspondence (KOC)—often referred to as the Kolmogorov–Obidi Master Correspondence Table—serves as a formal mapping that bridges algorithmic information theory and entropic field dynamics. [1]

Originated by John Onimisi Obidi in 2025, the theory elevates entropy from a statistical measure to a fundamental dynamical field ($S(x)$) that governs the universe. The KOC specifically establishes the following: [2, 3]

• Informational to Physical Mapping: It links Kolmogorov Complexity ($K(x)$), which measures the intrinsic information of individual objects, to the Obidi Action, a variational principle that defines how the entropic field evolves in physical spacetime.
• Structure of the Master Table: The correspondence table verifies the compliance of the "Six Pillars" of the theory, aligning mathematical constants and geometric structures with entropic field operators.
• Geodesic Derivation: It provides the mathematical lineage from Kolmogorov’s realization that dynamics generate information to the ToE assertion that entropy generates all dynamics, such as Entropic Geodesics. In this framework, gravity is reinterpreted as the tendency of the entropic field to minimize resistance, replacing traditional metric geodesics.
• Reinterpretation of Constants: The correspondence supports the "No-Rush Theorem," which reinterprets the speed of light ($c$) as the maximum rate at which the entropic field can reorganize information, rather than an arbitrary universal constant. [1, 2, 3, 4, 5]

The Theory of Entropicity (ToE) is currently an emerging proposal in theoretical physics, primarily documented through research papers and preprints on platforms like Encyclopedia MDPI and ResearchGate. [1, 6, 7]

Would you like to see the mathematical formulation of the Obidi Action or more details on the No-Rush Theorem (NRT)?

 

[1] https://www.researchgate.net

[2] https://medium.com

[3] https://medium.com

[4] https://entropicity.github.io

[5] https://medium.com

[6] https://encyclopedia.pub

[7] https://encyclopedia.pub

 

The Kolmogorov-Obidi Correspondence (KOC), often referred to within the broader Kolmogorov-Obidi Lineage (KOL), is a foundational concept in the 2026 Theory of Entropicity (ToE) proposed by John Onimisi Obidi. It represents a bridge between classical algorithmic information theory and modern entropic field theory. 

 

Here is an overview of the KOC within ToE:

 

Context: The Theory of Entropicity (ToE)

ToE proposes that entropy is not a byproduct of disorder, but the fundamental, dynamical field of reality from which gravity, space, time, and matter emerge. In this framework, the Obidi Action (c) acts as a variational principle, where entropy is the primary substrate. 

 

Kolmogorov-Obidi Correspondence (KOC) Explained

The KOC bridges Kolmogorov's algorithmic information complexity with Obidi's entropic field dynamics: 

• Foundation: It links Kolmogorov Complexity (the length of the shortest computer program that produces an object) to the Obidi Action (a variational principle governing the dynamics of the entropy field).
• Significance: It serves as a mathematical correspondence, suggesting that the "bits" of information required to describe a physical state (Kolmogorov) are fundamentally equivalent to the "entropy" needed to generate that state via the Obidi action.
• Evolution: The KOC positions ToE as the natural successor to traditional information-theoretic approaches, moving from "information as a description of objects" to "information as the dynamic substance of reality". 

 

Role in the Theory of Entropicity (ToE)

1. Fundamental Correspondence: It establishes that the minimum description length (Kolmogorov complexity) of a physical process corresponds to the minimal entropic action pathway derived from the Obidi Field equations.
2. Unification: Together with the Obidi Correspondence Principle (OCP), it helps bridge classical information theory, quantum mechanics, and gravity.
3. Consistency: It ensures that ToE remains consistent with classical information theory, treating established probability theories as special, coarse-grained limits of the more general, continuous entropic field. 

If you're interested in the mathematical details, we can explain to you:

• How the Obidi Action (c) connects specifically to information metrics.
• More about the Alemoh-Obidi Correspondence (AOC) mentioned in the documents.
• How ToE differs from Verlinde's Entropic Gravity.

Let us know which of these aligns with your interests.

"The Question of c" Introduced by Obidi from the Theory of Entropicity (ToE) in Modern Theoretical Physics: Consequences of the Alemoh-Obidi Correspondence (AOC)

"The Question of $c$" (TQoC) is a central concept in the Theory of Entropicity (ToE), a theoretical framework introduced by John Onimisi Obidi. [1, 2, 3]

The concept reinterprets the speed of light, denoted as $c$, not as a fundamental geometric constant of spacetime as in Einstein's relativity, but as an emergent property of a deeper "entropic field". [4, 5, 6]

The entropic limit interpretation of c in the Theory of Entropicity (ToE) is important because it restructures the foundations of relativity.

It is significant because it reframes the meaning of causality and the origin of spacetime.

Key Aspects of "The Question of $c$"

• Definition of $c$: In Obidi's theory, $c$ is defined as the maximum rate at which the entropic field can reorganize information.
• The No-Rush Theorem: Obidi introduces this theorem to explain why interactions cannot be instantaneous. It establishes $c$ as an entropic limit on how quickly entropy can reconfigure reality.
• Reconciliation of Scales: TQoC seeks to bridge classical and quantum physics by treating $c$ as a "speed limit" for the redistribution of entropy across a unified entropic manifold.
• Alternative to Spacetime Geometry: While standard physics views $c$ as a property of the geometry of the universe, Obidi argues it is a consequence of thermodynamic entropy. [4, 6, 7, 8, 9]

Context of the Theory

Obidi's work, formalized in documents like the Alemoh-Obidi Correspondence (AOC), replaces the Einstein Field Equations (EFE) with his own Master Entropic Equation (MEE) or Obidi Field Equations (OFE). This framework suggests that space, time, and matter are "macro-shadows" or excitations emerging from a more fundamental entropic field. [7, 10, 11, 12]

Would you like to explore the mathematical mechanics of the Obidi Action or how this theory addresses quantum gravity?

 

[1] https://www.cambridge.org

[2] https://encyclopedia.pub

[3] https://encyclopedia.pub

[4] https://medium.com

[5] https://notd.io

[6] https://client.prod.orp.cambridge.org

[7] https://medium.com

[8] https://www.researchgate.net

[9] https://d197for5662m48.cloudfront.net

[10] https://medium.com

[11] https://medium.com

[12] https://www.researchgate.net

 

"The Question of c" (TQoC) is a theoretical concept introduced by John Onimisi Obidi within his Theory of Entropicity (ToE), developed between 2025 and 2026. 

 

It reinterprets the speed of light (c) not as a fundamental, geometric constant of spacetime as proposed by Einstein, but as an emergent entropic limit. 

Core Aspects of The Question of c

• Definition: Obidi defines c as the maximum rate at which the entropic field can rearrange or redistribute information in the universe.
• Entropic Limit: Instead of being a limit imposed by the geometry of space, 
•  is a consequence of thermodynamic entropy.
• The No-Rush Theorem (NRT): This theorem within ToE states that no physical interaction can be instantaneous because of this finite, entropic speed limit.
• Distinction from Relativity: While Einstein's Relativity treats c as a fixed, universal constant, TQoC treats it as a "throughput rate" that can be, in certain theoretical contexts, viewed as a consequence of lower-level dynamics. 

Context within the Theory of Entropicity (ToE)

• The Alemoh-Obidi Correspondence (AOC): This concept was discussed in depth during exchanges between Obidi and Daniel Moses Alemoh, where Alemoh challenged Obidi to reconcile a finite speed of light with superluminal cosmic expansion, leading to this new interpretation.
• Mechanism: In ToE, gravity and time are considered emergent properties of entropy gradients, making the speed of light a necessary consequence of how entropy behaves.
• Redefining Foundations: The ToE program attempts to replace the geometric foundations of general relativity with an entropic framework. 

Obidi’s  Theory of Entropicity (ToE) represents a radical departure from standard physics, aiming to unify information theory and gravity through the behavior of entropy. 

"The Question of c" (TQoC) is a theoretical concept introduced by John Onimisi Obidi within his Theory of Entropicity (ToE), developed between 2025 and 2026. 

 

It reinterprets the speed of light (c) not as a fundamental, geometric constant of spacetime as proposed by Einstein, but as an emergent entropic limit. 

 

Core Aspects of The Question of c

• Definition: Obidi defines c as the maximum rate at which the entropic field can rearrange or redistribute information in the universe.
• Entropic Limit: Instead of being a limit imposed by the geometry of space, c is a consequence of thermodynamic entropy.
• The No-Rush Theorem: This theorem within ToE states that no physical interaction can be instantaneous because of this finite, entropic speed limit.
• Distinction from Relativity: While Einstein's Relativity treats c as a fixed, universal constant, TQoC treats it as a "throughput rate" that can be, in certain theoretical contexts, viewed as a consequence of lower-level dynamics. 

 

Context within ToE

• The Alemoh-Obidi Correspondence (AOC): This concept was discussed in depth during exchanges between Obidi and Daniel Moses Alemoh, where Alemoh challenged Obidi to reconcile a finite speed of light with superluminal cosmic expansion, leading to this new interpretation.
• Mechanism: In ToE, gravity and time are considered emergent properties of entropy gradients, making the speed of light a necessary consequence of how entropy behaves.
• Redefining Foundations: The ToE program attempts to replace the geometric foundations of general relativity with an entropic framework. 

Obidi’s ToE represents a radical departure from standard physics, aiming to unify information theory and gravity through the behavior of entropy. 

 

"The Question of c" (TQoC) is a central concept in John Onimisi Obidi's Theory of Entropicity (ToE), formulated between 2025 and 2026 to recontextualize the speed of light (c) as an emergent entropic limit rather than merely a constant of spacetime geometry. 

 

Here is a breakdown of the key aspects of Obidi's Question of c:

• Definition of c: In ToE, cis redefined as the maximum rate at which the entropic field can reorganize information, serving as the universal "Entropic Speed Limit" (ESL).
• Fundamental Shift: While relativity views c as a rule of spacetime geometry, TQoC proposes that c is a consequence of thermodynamic entropy.
• The No-Rush Theorem: This theorem within the theory states that no physical interaction can be instantaneous, because the entropic field requires a specific rate of reconfiguration to maintain causal order.
• Causality and Order: The constant c is interpreted as the "logical horizon of causality," ensuring that effects cannot occur before their causes within the entropic field's update rate.
• Origin: The concept was heavily developed in the Alemoh-Obidi Correspondence (AOC) in early 2026, where Daniel Alemoh challenged Obidi to reconcile a finite speed of light with cosmological expansion. 

The Theory of Entropicity argues that space, time, and matter are emergent properties of these entropic gradients, with c being the boundary that defines what can be known in time. 

Reference 

The GitHub /Cloudflare Canonical Archives of the Theory of Entropicity (ToE):

The Theory of Entropicity (ToE)

https://entropicity.github.io/Theory-of-Entropicity-ToE/

https://entropicity.github.io/Theory-of-Entropicity-ToE/papers/

https://entropicity.github.io/Theory-of-Entropicity-ToE/docs/The-Theory-of-Entropicity-(ToE)-Living-Review-Letters-Series-Letter-IC-The-Alemoh-Obidi-Correspondence-(AOC)-U1_April-26-2026.pdf

https://doi.org/10.13140/RG.2.2.23920.83207

https://doi.org/10.17605/OSF.IO/8JHF2

Zenodo:

https://doi.org/10.5281/zenodo.19803329

Obidi, J. O. (2026). The Theory of Entropicity (ToE) Living Review Letters Series — Letter IC: The Alemoh-Obidi Correspondence on the Foundations of the Theory of Entropicity (ToE), Monograph — Volume I, Part 1, Communications on the Formulation and Conceptual Architecture of ToE (Version V1).

Zenodo. https://doi.org/10.5281/zenodo.19803329

Obidi, J. O. (2026). The Theory of Entropicity (ToE) Living Review Letters Series — Letter IC: The Alemoh-Obidi Correspondence on the Foundations of the Theory of Entropicity (ToE), Monograph — Volume I, Part 1, Communications on the Formulation and Conceptual Architecture of ToE (Version 2).

Zenodo. https://doi.org/10.5281/zenodo.19804619

Zenodo Book:

Obidi, J. O. (2026). The Theory of Entropicity (ToE) Living Review Letters Series — Letter IC: The Alemoh-Obidi Correspondence on the Foundations of the Theory of Entropicity (ToE), Monograph — Volume I, Part 1, Communications on the Formulation and Conceptual Architecture of ToE (Version V1) [Book]. Zenodo. https://doi.org/10.5281/zenodo.19803791

The Question of c — A New Meaning of Light and the Speed of Light Introduced by the Theory of Entropicity (ToE)

In the Theory of Entropicity (ToE), developed by John Onimisi Obidi in 2025, the constant $c$ (the speed of light) is reinterpreted as the maximum rate of entropic rearrangement. Unlike standard Einsteinian relativity, which treats $c$ as a starting postulate (an "unexplained given"), ToE derives its constancy and value as a physical necessity of a universal "entropic field". [1, 2, 3, 4]

Key aspects of the "question of $c$" in this framework include:

• Derivation vs. Postulation: ToE argues that $c$ is not a geometric axiom but a thermodynamic consequence. It emerges from the Master Entropic Equation (MEE), where entropic disturbances are shown to propagate at a characteristic speed $c$ along the null cone of spacetime.
• The "No-Rush Theorem": This core principle (also referred to as G/NCBR—"Nature cannot be rushed") states that all physical interactions require a finite, non-zero time for the entropic field to redistribute and synchronize states. This finite rate of information and energy redistribution is exactly what manifests as the speed of light.
• The "Movie Screen" Analogy: ToE suggests that the entropic field acts like a "movie screen" with an absolute refresh rate ($c$). Observers, clocks, and rulers are themselves "projections" of this field. When an observer moves through the field, their tools (clocks and rulers) are physically altered by "entropic stress," which ensures that any measurement of $c$ remains constant.
• Physical Grounding for Relativity: Relativistic effects like time dilation and length contraction are viewed as physical "entropic resistances" to motion. Moving systems divert entropic resources to maintain structural integrity against "entropic drag," leaving less "budget" for internal clock cycles (time dilation). [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]

In summary, the Theory of Entropicity treats light not as the cause of the universal speed limit, but as a "tracer" or "manifestation" of the deepest law of the universe: the finite processing speed of entropy. [16, 17]

Would you like to explore the mathematical foundations of the Master Entropic Equation or see how this theory explains quantum entanglement delays?

 

[1] https://www.authorea.com

[2] https://medium.com

[3] https://encyclopedia.pub

[4] https://www.cambridge.org

[5] https://medium.com

[6] https://encyclopedia.pub

[7] https://www.authorea.com

[8] https://www.cambridge.org

[9] https://medium.com

[10] https://encyclopedia.pub

[11] https://medium.com

[12] https://encyclopedia.pub

[13] https://encyclopedia.pub

[14] https://encyclopedia.pub

[15] https://medium.com

[16] https://medium.com

[17] https://medium.com

 

The Canonical Archives of the Theory of Entropicity (ToE): The GitHub and Cloudflare Archives of the Theory of Entropicity (ToE)

The canonical archive of the Theory of Entropicity (ToE), formulated by John Onimisi Obidi, is located at https://entropicity.github.io/Theory-of-Entropicity-ToE/. [1, 2]

This repository serves as the official, version-controlled repository containing the monograph and foundational writings. The theory, which emerged in 2025-2026, posits that entropy is the fundamental, primary ontological field from which geometry, matter, and spacetime emerge, rather than a derived statistical quantity. [2, 3, 4]

Core Components of the Archive:

• Monograph: The main text presenting the Theory of Entropicity (ToE).
• Concepts: Core definitions including Obidi’s Ontodynamics, Entrodynamics, and the Multi-stage Multi-phase Diffusion Pipeline Model (MSMPDPM).
• Equations: The Master Entropic Equation (MEE), Obidi Action, and Obidi Field Equations (OFE).
• Letters: The "ToE Living Review Letters Series" on platforms like Medium or ResearchGate detailing the theory's foundations. [2, 4, 5, 6]

Other Official Channels:

• Google Live Site: https://theoryofentropicity.blogspot.com
• YouTube Channel: @TheoryofEntropicityToE
• Notion Workspace: Obidi's Foundational Physics Manifesto [1, 7]

The theory is heavily based on information geometry and aims to unify thermodynamics, quantum mechanics, and relativity under a single entropic framework. [8, 9, 10, 11, 12]

Would you like me to help you find specific equations, or rather look for the latest Living Review Letter in the archive?

References 

[1] https://music.youtube.com

[2] https://theory-of-entropicity-toe.pages.dev

[3] https://medium.com

[4] https://medium.com

[5] https://www.researchgate.net

[6] https://www.researchgate.net

[7] https://medium.com

[8] https://medium.com

[9] https://www.cambridge.org

[10] https://www.researchgate.net

[11] https://osf.io

[12] https://link.springer.com

The canonical archive of the Theory of Entropicity (ToE), developed by John Onimisi Obidi, is primarily hosted on GitHub. It is designed to serve as the foundational repository for the theory, which proposes that entropy is the fundamental ontological field from which geometry, matter, and physical laws emerge. 

Key Repository Locations

• Canonical Github Archive: Theory of Entropicity (ToE) GitHub Pages
• Alternative/Mirror Repository: entropicity.github.io
• Blogger Archive: Theory of Entropicity (ToE) Blog 

Contents of the Archive

The archive organizes the development of the theory into several key areas:

• Monograph: The main, structured presentation of the Theory of Entropicity (ToE).
• Concepts: Core definitions and philosophical foundations, including the, "Obidi Conjecture," which states that entropy is the fundamental dynamical field.
• Equations: Mathematical structures, including the "Master Entropic Equation (MEE)" and "Obidi Field Equations (OFE)".
• Papers: Links to formal publications and preprints hosted on platforms such as Cambridge Open Engage, ResearchGate, and Medium.
• Diagrams & Notes: Visual interpretations of entropic gradients and development notes. 

The theory aims to replace the foundational role of spacetime geometry with an "entropic field," with the archive acting as a record of its development beginning in 2025. 

"The Question of c" in the Theory of Entropicity (ToE): Implications of the Alemoh-Obidi Correspondence (AOC) for the Speed of Light and Its Generalized Meaning in Modern Theoretical Physics 

In the Theory of Entropicity (ToE), a framework primarily developed by John Onimisi Obidi in 2025, the constant $c$ is reinterpreted from a geometric postulate into a physical consequence of the universe's fundamental "entropic field". [1, 2]

Instead of treating the speed of light ($c$) as an arbitrary constant of spacetime, ToE defines it as the maximum rate at which the entropic field can reorganize energy and information. [3, 4]

The Reinterpretation of $c$

In standard physics, $c$ is a fixed speed limit. In ToE, $c$ is the "speed of causality" determined by the intrinsic properties of the entropic field, much like the speed of sound is determined by the properties of the air it travels through. [2, 5, 6]

• Maximum Refresh Rate: The theory views the universe as an informational system. $c$ represents the universal "refresh rate" or the fastest possible "entropic handshake" between two systems.
• Constitutive Law: ToE proposes that $c$ is derived from the ratio of two field properties: entropic conductivity ($\chi_0$) and entropic capacity ($C_0$).
  • $\chi_0$ measures how readily entropy flows.
  • $C_0$ measures how much entropy the field can store or resist.
  • The ratio of these two dictates the speed at which disturbances (like light) propagate. [2, 7, 8, 9, 10]

Why Light Moves at $c$

According to ToE, light is not the cause of the speed limit; it is simply a massless manifestation that "saturates" the field's maximum reconfiguration rate. The "speed limit" exists because the entropic field itself cannot be rearranged instantaneously. [2, 7, 11, 12]

Consequences of the Entropic $c$

The theory uses this entropic definition to provide physical mechanisms for effects that Einstein described as geometric: [13, 14]

• The No-Rush Theorem: This core principle states that no interaction can be instantaneous. Every event requires a finite time for the entropic field to redistribute and synchronize states.
• Time Dilation: Moving through the entropic field requires a "budget" of entropy. A moving object uses part of its entropic capacity for motion, leaving less for its internal processes (like a clock ticking), which causes time to slow down.
• Relativistic Mass: Mass increase is seen as Entropic Resistance (ERP). As an object approaches $c$, the "entropic gradient" it faces becomes steeper, requiring near-infinite entropy to move faster. [2, 5, 15, 16, 17]

Would you like to explore the mathematical framework (such as the Master Entropic Equation) or how this theory attempts to unify gravity and quantum mechanics?

 

[1] https://medium.com

[2] https://medium.com

[3] https://medium.com

[4] https://encyclopedia.pub

[5] https://encyclopedia.pub

[6] https://www.vaia.com

[7] https://medium.com

[8] https://medium.com

[9] https://encyclopedia.pub

[10] https://medium.com

[11] https://medium.com

[12] https://medium.com

[13] https://encyclopedia.pub

[14] https://www.cambridge.org

[15] https://encyclopedia.pub

[16] https://encyclopedia.pub

[17] https://medium.com

 

In the Theory of Entropicity (ToE), a framework primarily developed by John Onimisi Obidi in 2025, the constant $c$ is reinterpreted from a geometric postulate into a physical consequence of the universe's fundamental "entropic field". [1, 2]

Instead of treating the speed of light ($c$) as an arbitrary constant of spacetime, ToE defines it as the maximum rate at which the entropic field can reorganize energy and information. [3, 4]

The Reinterpretation of $c$

In standard physics, $c$ is a fixed speed limit. In ToE, $c$ is the "speed of causality" determined by the intrinsic properties of the entropic field, much like the speed of sound is determined by the properties of the air it travels through. [2, 5, 6]

• Maximum Refresh Rate: The theory views the universe as an informational system. $c$ represents the universal "refresh rate" or the fastest possible "entropic handshake" between two systems.
• Constitutive Law: ToE proposes that $c$ is derived from the ratio of two field properties: entropic conductivity ($\chi_0$) and entropic capacity ($C_0$).
  • $\chi_0$ measures how readily entropy flows.
  • $C_0$ measures how much entropy the field can store or resist.
  • The ratio of these two dictates the speed at which disturbances (like light) propagate. [2, 7, 8, 9, 10]

Why Light Moves at $c$

According to ToE, light is not the cause of the speed limit; it is simply a massless manifestation that "saturates" the field's maximum reconfiguration rate. The "speed limit" exists because the entropic field itself cannot be rearranged instantaneously. [2, 7, 11, 12]

Consequences of the Entropic $c$

The theory uses this entropic definition to provide physical mechanisms for effects that Einstein described as geometric: [13, 14]

• The No-Rush Theorem: This core principle states that no interaction can be instantaneous. Every event requires a finite time for the entropic field to redistribute and synchronize states.
• Time Dilation: Moving through the entropic field requires a "budget" of entropy. A moving object uses part of its entropic capacity for motion, leaving less for its internal processes (like a clock ticking), which causes time to slow down.
• Relativistic Mass: Mass increase is seen as Entropic Resistance (ERP). As an object approaches $c$, the "entropic gradient" it faces becomes steeper, requiring near-infinite entropy to move faster. [2, 5, 15, 16, 17]

Would you like to explore the mathematical framework (such as the Master Entropic Equation) or how this theory attempts to unify gravity and quantum mechanics?

 

[1] https://medium.com

[2] https://medium.com

[3] https://medium.com

[4] https://encyclopedia.pub

[5] https://encyclopedia.pub

[6] https://www.vaia.com

[7] https://medium.com

[8] https://medium.com

[9] https://encyclopedia.pub

[10] https://medium.com

[11] https://medium.com

[12] https://medium.com

[13] https://encyclopedia.pub

[14] https://www.cambridge.org

[15] https://encyclopedia.pub

[16] https://encyclopedia.pub

[17] https://medium.com

 

 

In the Theory of Entropicity (ToE), originated by John Onimisi Obidi in 2025, the "question of c" (the speed of light) is reinterpreted from an unexplained postulate into a derived consequence of thermodynamics. 

The ToE moves beyond treating entropy as a passive measure of disorder, defining it instead as a fundamental, dynamic field that permeates the universe. 

The Core Reinterpretation of c

• Maximum Rate of Realignment: ToE proposes that c is the maximum rate at which the universal Entropic Field can reconfigure or redistribute energy and information.
• Light as a Symptom: Light is not deemed to "travel" in the traditional sense, but rather acts as the visible manifestation of this entropic rearrangement speed.
• The "No-Rush Theorem": A foundational principle in ToE stating that "nature cannot be rushed"—no physical interaction or information transfer can exceed the rate at which the entropic field updates. 

ToE vs. Einstein's Relativity

Where Einstein took the constancy of the speed of light (c) as a postulate to build his theory, the Theory of Entropicity (ToE) attempts to derive this constancy as a thermodynamic law. 

Concept	Relativity (ToR)	Theory of Entropicity (ToE)
Speed of Light (c)	A fundamental, postulated universal constant.	The maximum rate of entropic reconfiguration (an emergent property).
Why c is a Limit	Axiom of nature.	"No-Rush Theorem": The entropic field has a maximum processing speed.
Relativistic Effects	Kinematic necessity of space/time geometry.	Entropic resistance to motion; energy is used up to move, leaving less for internal time.

Implications of ToE on 

• Causality Enforcement: The finite rate of entropic redistribution (c) ensures that effects cannot occur before their causes, maintaining consistent causality.
• Entropic Resistance: Moving through the entropic field causes "entropic drag," which explains why objects with mass cannot reach c. As speed nears c, entropic costs become prohibitive.
• Redefining Gravity: Entropic Gravity implies that gravity is not a force but a result of entropic gradients (pressure) in the field that also propagate at c.

In summary, the Theory of Entropicity (ToE) claims that is the "heartbeat of existence"—the universal rhythm of entropic change, rather than just the speed of a photon, as described in this Encyclopedia.pub entry. 

 

 

In the Theory of Entropicity (ToE), developed by John Onimisi Obidi (2025), the question of c is a fundamental reinterpretation of the speed of light. Instead of treating c as an arbitrary, fundamental constant of spacetime geometry (as in Special Relativity), ToE derives c as an emergent, thermodynamic property of the entropic field. 

Here is a breakdown of the question of c within this framework:

1. From Postulate to Entropic Limit

• Einstein's View: c is a postulate—the maximum speed for all massless signals, taken as a foundational axiom of the universe's geometry.
• ToE View: c is the maximum rate at which the "Entropic Field"—the fundamental, physical substrate of the universe—can reorganize itself to redistribute energy and information.
• The "No-Rush Theorem": ToE proposes that nature "cannot be rushed," forbidding superluminal (faster-than-light) processes because entropic realignment takes finite, non-zero time. 

2. Light as a "Tracer" of Entropy

• In ToE, the speed of light is not about photons themselves, but about the speed at which entropic changes propagate.
• Light is merely the visible manifestation of this maximum speed of entropic reconfiguration.
• The "speed of light" is reinterpreted as the "fastest possible entropic handshake". 

3. Relativity as Entropic Inevitability

• Mass Increase/Time Dilation: These are reinterpreted as physical entropic resistances to motion. Moving through the entropic field requires the reconfiguration of the field; as velocity approaches c, this "entropic cost" diverges.
• Constant Speed: The invariance of c
•  is a thermodynamic consequence of the entropic field’s "null cone," rather than a geometric given. 

Summary of the "Question of C" in ToE

Feature	Einsteinian Relativity (ToR)	Theory of Entropicity (ToE)
Status of c	Fundamental Postulate	Emergent Thermodynamic Law
Origin of c	Geometry of Spacetime	Entropic Field Dynamics
Meaning of c	Max speed of light	Max rate of information update
What is c?	A universal constant	"Entropic Cost of Motion" limit

Proponents of this recent theory (as of 2025–2026) suggest that this approach reconciles quantum mechanics and relativity by providing a physical, rather than purely geometric, basis for universal constraints. 

The Question of c: How the Theory of Entropicity (ToE) Interprets the Speed of Light in Einstein’s Second Postulate of the Special Theory of Relativity (SToR)

A Comprehensive Exposition in the Spirit of the Alemoh–Obidi Correspondence (AOC)

Part I — The Historical and Conceptual Problem of c

Few constants in physics have carried as much conceptual weight as the speed of light, c.

In Einstein’s 1905 formulation of the Special Theory of Relativity (SToR), c appears not merely as a property of electromagnetism but as a universal invariant, a structural constant of spacetime itself. Einstein’s Second Postulate states:

The speed of light in vacuum has the same value in all inertial frames, independent of the motion of the source.

This postulate—simple, elegant, and revolutionary—became the cornerstone of relativistic kinematics. Yet, from the beginning, it raised a profound question:

Why should the speed of light be invariant?

Why should a constant arising from Maxwell’s electrodynamics suddenly become the defining invariant of spacetime structure?

Einstein himself never derived c from deeper principles.

He postulated it.

The 20th century accepted this postulate as a primitive truth.

The 21st century began to question it.

And the Theory of Entropicity (ToE), as articulated in the Living Review Letters Series Letter IC, takes the boldest step yet:

1. ToE does not assume the invariance of c.
2. ToE derives the invariant speed from the entropic field itself.

This is the heart of the “Question of c” in ToE.

Part II — The Entropic Field and the Obidi Action

The Theory of Entropicity begins from a radically different ontological starting point:

1. - Entropy is not a derived quantity. 
2. - Entropy is not a statistical artifact. 
3. - Entropy is not a thermodynamic bookkeeping device.

Entropy is the fundamental field of the universe.

From this field, denoted (S(x) ), the ToE constructs:

1. - an induced information metric (g(S)) 
2. - an entropic curvature scalar (R_{IG}[S]) 
3. - a Boltzmann‑weighted kinetic term (e^{S/k_B}(∆S)^2) 
4. - and the full dynamical action known as the Obidi Action

The Obidi Action is the entropic analogue of the Einstein–Hilbert action, but deeper:

it does not assume spacetime geometry—it generates it.

This is the decisive conceptual move that distinguishes ToE from all prior frameworks, including Bianconi, Jacobson, Padmanabhan, Verlinde, and holographic approaches.

Part III — The Emergence of a Propagation Speed from the Entropic Field

From the Obidi Action, the Euler–Lagrange variation yields a wave‑type equation for the entropic field:

Box_{IG} S = {(entropic source terms)}

The structure of this equation contains a characteristic propagation speed, which Obidi identifies as:

c_e = √{{X}/{C}}

where:

- (X) is the entropic stiffness

- (C) is the entropic capacity

These quantities arise naturally from the functional derivatives of the Obidi Action.

They are not inserted by hand.

They are not analogies.

They are not metaphors.

They are intrinsic properties of the entropic field.

Thus:

The entropic field has a natural propagation speed.

This speed is not assumed.

It is not postulated.

It is not borrowed from Maxwell.

It is derived.

Part IV — The ToE Interpretation of Einstein’s c

Here is the central insight of the ToE:

> Einstein’s invariant speed c is the propagation speed of the entropic field in the physical regime where electromagnetism is emergent.

In other words:

- Maxwell’s c = 1/√{(mu_0)(epsilon_0)}

- Obidi’s c_e = √{X/C}

are two manifestations of the same underlying invariant speed, expressed in different physical languages.

Maxwell’s c is the electromagnetic expression.

Obidi’s cₑ is the entropic expression.

In the physical regime corresponding to our universe:

c_e = c

But ToE goes further:

In other entropic regimes, (c_e) may differ from (c).

This is the first theoretical framework to allow a principled, non‑speculative variation of the invariant speed, grounded in entropic geometry rather than arbitrary modification of relativity.

This is the “Question of c” in its deepest form.

Part V — Why This Matters

Einstein’s Second Postulate becomes, in ToE:

The invariant speed of relativistic kinematics is the propagation speed of the entropic field.

This is not a replacement of Einstein.

It is a completion of Einstein.

Einstein postulated the invariance of c.

ToE explains it.

Einstein assumed the metric structure of spacetime.

ToE derives it from entropy.

Einstein took the speed of light as fundamental.

ToE shows it is emergent.

This is the conceptual revolution at the heart of the Alemoh–Obidi Correspondence (AOC).

Part VI — Coming Next

The next parts will cover:

1. - The full derivation of (c_e) from the Obidi Action
2. - The entropic cone vs. Einstein’s light cone
3. - How Lorentz symmetry emerges from entropic flux conservation
4. - The correspondence between Maxwell’s (c) and Obidi’s (c_e)
5. - The philosophical implications for the ontology of spacetime
6. - How the AOC frames the “Question of c” historically and conceptually

In essence, the Theory of Entropicity (ToE) is a bold, unified, and mathematically ambitious attempt to rethink the foundational structures of the universe. 

What is Actually Unique About the Theory of Entropicity (ToE)?

The Theory of Entropicity (ToE), developed by John Onimisi Obidi, is distinguished by several genuinely unique features that set it apart from other entropic or information-based approaches to physics. Here is what is actually unique about it:

1. Entropy as a Fundamental Physical Field

The most radical claim of ToE is that entropy is not merely a statistical measure of disorder, but a continuous, dynamical physical field — the "Entropic Field" — that constitutes the primordial substrate of reality.   This is an ontological reversal: instead of entropy being a shadow cast by matter and energy, it is the "light source" itself. Space, time, mass, and motion are reinterpreted as emergent configurations or excitations of this underlying entropic field. 

This goes beyond prior entropic theories. For example, Erik Verlinde's entropic gravity treats gravity as an emergent entropic force but does not elevate entropy to a field.  Ginestra Bianconi's gravity-from-entropy framework introduces an entropic action but still treats entropy as a derived measure.  ToE is unique in literally making entropy the field. 

2. A Unique Combination of Structural Features

No prior framework combines the following elements into a single coherent architecture: 

Feature Prior Theories ToE

Entropy as a physical field No Yes

Bodies move through an entropic field No Yes

Motion minimizes entropic resistance No Yes

Explicit entropic action Some (Bianconi) Yes

Field equations for entropy Some (Bianconi) Yes

Entropic geodesics No Yes

While individual elements like an entropic action appear in earlier works, the combination of entropy-as-field, entropic action, entropic field equations, and entropic geodesics is unique to ToE. 

3. Derivation of the Speed of Light from First Principles

Einstein postulated the constancy of the speed of light (c) as an axiom. ToE claims to derive c as an emergent property — specifically, as the maximum rate at which the entropic field can reorganize energy and information.   This is formalized by the No-Rush Theorem (NRT), which states that no physical interaction can occur instantaneously because the entropic field itself has a finite processing speed.  

In this view, c is not just the speed of photons but the "heartbeat of existence" — the universal rhythm of the entropic field. 

4. The Obidi Action and Master Entropic Equation (MEE)

ToE is built on a rigorous mathematical foundation with two complementary action principles: 

- Local Obidi Action (LOA): Integrates curvature, asymmetric transport, and entropy gradients to describe how the entropic field generates local geometry.

- Spectral Obidi Action (SOA): Encodes global constraints through the spectrum of the entropic field.

From these emerges the Master Entropic Equation (MEE), which serves as the governing field equation for entropy — analogous to Einstein's field equations for gravity, but with entropy as the primary driver of curvature.  Notably, the MEE is inherently iterative rather than solvable in closed form, reflecting the step-by-step nature of entropic updating (like Bayesian inference). 

5. A Mechanistic Explanation for Relativistic Effects

Rather than treating time dilation and length contraction as geometric consequences of a postulated constant c, ToE offers a physical mechanism:  

- Time dilation: Motion through the entropic field consumes the entropic budget, suppressing internal timekeeping cycles.

- Length contraction: Entropy allocated to structural maintenance is reallocated to motion.

- Mass increase: Increased entropic drag/resistance as the field reconfigures at higher speeds.

This shifts the explanatory arrow from "If c is constant, then time must slow down" to "Because moving through the entropic field slows time, c is measured to be constant." 

6. Unification Through Information Geometry

ToE employs sophisticated mathematical tools from information geometry — including the Fisher-Rao metric, Fubini-Study metric, and Amari-Čencov α-connections — to link informational divergence to physical curvature.  The Obidi Curvature Invariant (OCI = ln 2) is proposed as the smallest unit of entropic cost, suggesting that existence itself requires a quantifiable entropic expenditure. 

7. The No-Rush Theorem (NRT): A Universal Lower Bound on Interaction Time

The No-Rush Theorem asserts that every physical process must have a finite, non-zero duration because the entropic field cannot change instantaneously.  This provides a physical mechanism for causality and implies that wavefunction collapse and entanglement formation are not instantaneous but occur over finite, attosecond-scale intervals. 

Summary

What is actually unique about ToE is its structural completeness: it is the only framework that (a) treats entropy as a fundamental dynamical field with its own action and field equations, (b) derives c and relativistic effects from that field's dynamics rather than postulating them, and (c) unifies these features with information geometry into a single coherent architecture. Whether these claims hold up to experimental scrutiny remains to be seen — the theory is still emerging and awaits rigorous validation.

In essence, the Theory of Entropicity (ToE) is a bold, unified, and mathematically ambitious attempt to rethink the foundational structures of the universe.