The Theory of Entropicity (ToE) Explained on a Classroom Chalkboard with Great Scholarship 

The chalkboard in the image displays equations and terms from a recent, speculative framework in theoretical physics called the Theory of Entropicity (ToE), proposed by researcher John Onimisi Obidi around 2025. [1, 2]

Key Chalkboard Terms and Equations

The text on the board relates to the fundamental "accounting" system of this theory:

• Obidi Action ($S$ or $I_S$): This is the theory's core variational principle, analogous to the Einstein-Hilbert action in general relativity. It defines how the "entropy field" evolves and dictates the path of least entropic cost for all physical processes.
• $CI = (n_2)$ (Obidi Curvature Invariant): In ToE, $OCI = \ln 2$ is considered the smallest "unit" of entropic cost. It represents a fundamental scale for reality, suggesting that every physical interaction requires a minimum "payment" of entropy. The notation on the board $(n_2)$ is likely a shorthand for the natural logarithm of 2 ($\ln 2$).
• $Ci = \ln^2 2$: This represents a higher-order calculation of entropic cost or divergence used within the theory's mathematical framework to describe how the entropic field reconfigures during interactions. [3, 4, 5, 6]

Core Tenets of the Theory of Entropicity

As noted in the image's overlay text, the theory attempts to re-evaluate the foundations of physics by making entropy—rather than mass, energy, or spacetime—the primary substrate of the universe: [7, 8]

• Emergent Gravity and Spacetime: Gravity and the geometry of space are not fundamental but emerge from the flow and gradients of a dynamic entropy field.
• Speed of Light ($c$): The theory derives $c$ as the maximum rate at which the entropic field can rearrange information. It is the "heartbeat" of existence rather than an arbitrary speed limit.
• Quantum Reinterpretation: ToE redefines Quantum Entanglement and Wavefunction Collapse as finite-duration entropic processes. It rejects the idea of "spooky action at a distance" by proposing that these correlations take a tiny but non-zero amount of time (roughly 232 attoseconds) to form.
• The No-Rush Theorem: This principle states that no physical interaction can occur instantaneously; everything requires a finite amount of "entropic processing time". [1, 2, 9, 10, 11, 12]

Scientific Context

The Theory of Entropicity (ToE) is a modern, alternative theory that seeks to unify thermodynamics, relativity, and quantum mechanics under a single "entropic monism". While it uses rigorous and sophisticated mathematical tools from information geometry, it is currently an audacious and provocative proposal rather than a standard, widely theory in the traditional academic physics community. [5, 7, 8, 11]

Would you like a deeper breakdown of how this theory attempts to solve the famous Einstein "spooky action at a distance" problem in quantum mechanics?

The No-Go Theorem (NGT) of the Theory of Entropicity (ToE)

The Entropic No-Go Theorem (NGT) in John Onimisi Obidi’s radical Theory of Entropicity (ToE) posits that no physical process can outrun or shortcut the finite, causal structure of the universe's entropic field.

 Formally stated as

, it forbids instantaneous action, forcing all processes to obey a maximum entropic propagation rate, treating entanglement not as "spooky action," but as a finite-time, entropy-mediated event. 

Key Aspects of the NGT in ToE

• Fundamental Constraint: The NGT acts as a universal impossibility theorem, similar in function to Bell-type theorems but grounded in entropic causality, restricting any process from extending beyond the "entropic causal cone" (
  

  $$
  ).
• No-Rush Theorem (NRT): A core component of the NGT that mandates a non-zero, minimum interaction time for all physical processes, stating that the universe cannot be "rushed".
• Entropic Field Dynamics: The ToE redefines entropy from a statistical measurement to a dynamic, physical field that generates spacetime and governs the speed of information.
• Resolution of Paradoxes: By limiting information transfer to the finite speed of entropic reconfiguration (identified with 
  

  $$
  ), the NGT reconciles quantum entanglement and relativity, removing the need for instantaneous action. 

The Theory of Entropicity (ToE), proposed as an alternative, audacious framework, asserts that entropy is the fundamental, generative substrate for all physical reality. 

Would you like more details on how the No-Rush Theorem specifically applies to quantum decoherence?

What are the Formulations, Differences and Utilities of the Polyakov Action, Einstein-Hilbert Action, Nambu-Goto Action and the General Obidi Action (LOA + SOA) of the Theory of Entropicity (ToE)?

---

Abstract

We propose that spacetime geometry and string‑like dynamics arise as effective projections of a deeper entropic manifold governed by the General Obidi Action (GOA). In this framework, the fundamental degrees of freedom are entropic rather than geometric, and the familiar structures of general relativity and worldsheet theory emerge through coarse‑graining and projection. We show that the Local Obidi Action reduces to the Einstein–Hilbert action under entropic dimensional reduction, while the Structural Obidi Action yields a Polyakov‑type worldsheet action for embedded entropic structures. This establishes a unified, entropic origin for both spacetime curvature and string‑like excitations, suggesting that distinguishability, curvature, and quantum behavior share a common entropic foundation.

Introduction

The Theory of Entropicity (ToE) posits that entropy is not a derived quantity but the primary organizing principle of physical reality. Instead of beginning with spacetime, fields, or strings, ToE begins with an entropic manifold whose geometry encodes distinguishability, information flow, and the ln 2 threshold that separates physical states from indistinguishable configurations. Spacetime and quantum behavior arise not as fundamental structures but as emergent shadows of this deeper entropic geometry.

In this work, we formalize this emergence using the General Obidi Action, which consists of a local entropic curvature term (LOA) and a structural term governing embedded entropic configurations (SOA). We demonstrate that, under natural projection and coarse‑graining assumptions, LOA reduces to the Einstein–Hilbert action of general relativity, while SOA reduces to a Polyakov‑type action familiar from string theory. This provides a unified entropic origin for both gravitational and string‑like dynamics, framing them as effective descriptions of a single underlying entropic manifold.

The Key Differences Between the Polyakov Action (PA), Einstein-Hilbert Action (E-HA), and the Local Obidi Action (LOA) of the Theory of Entropicity (ToE) 

The key differences between the Polyakov action, Einstein-Hilbert action, and the Local Obidi Action (LOA) lie in their fundamental objects of study, dimensionality, and physical goals, ranging from describing string dynamics to the curvature of spacetime and unified entropic theories.

The Polyakov Action (P): 

Describes the 2D worldsheet of a string moving through a higher-dimensional spacetime. It is quadratic in derivatives, making it ideal for string quantization, and it is classically equivalent to the Nambu-Goto action, which represents the area of the worldsheet.

Einstein-Hilbert Action (E-H): 

The foundational action for General Relativity, which describes the 4D spacetime metric and its curvature (Ricci scalar). Its stationary points yield the Einstein field equations, relating spacetime geometry to energy content.

Local Obidi Action (LOA): 

A modern theoretical framework (Theory of Entropicity) that posits gravity and quantum phenomena as emergent from a fundamental entropy field, S(x). Unlike the standard actions, it explicitly incorporates irreversible, non-equilibrium dynamics (time arrow) into the action itself.

Detailed Comparison Table:

Feature Polyakov Action ()Einstein-Hilbert () Local Obidi Action (LOA)
Object of Study 2D Worldsheet (Strings) 4D Spacetime Metric Entropic Field ()
Primary Symmetry Diffeomorphism + Weyl Diffeomorphism Invariance Entropic/General Covariance
Key Equation String Equations of Motion Einstein Field Eq () Master Entropic Eq (MEE)
Quantization Excellent (Quadratic) Very Difficult (Non-renormalizable) Unified (Unifies QM & GR)
Distinction Area minimization of string Curvature of spacetime Entropic gradients/gravity


Differences in Focus

Polyakov vs. Einstein-Hilbert: 

The Polyakov action acts on a 2D worldsheet (internal to string theory) to calculate scattering amplitudes, whereas Einstein-Hilbert acts on the 4D spacetime manifold.

Emergent vs. Fundamental: 

Einstein-Hilbert treats spacetime geometry as fundamental. In contrast, the LOA treats spacetime and gravity as emergent properties of the fundamental entropy field.

Equilibrium vs. Non-Equilibrium: 

While P and E-H are generally time-symmetric, the LOA explicitly builds irreversible processes (entropy flow) into the action, suggesting that energy conservation is an emergent consequence of maximizing entropy rather than a fundamental starting point.

Contextual Notes

Obidi Action: 

A 2025/2026 theoretical framework ["Theory of Entropicity  (ToE)"] developed to bridge quantum mechanics and General Relativity.

Polyakov Action equivalence: 

By "integrating out" the auxiliary metric in the Polyakov action, it becomes equivalent to the Nambu-Goto action.

The Local Obidi Action (LOA) reinterprets the "constant" speed of light as the maximum rate at which the entropic field can rearrange, redefining relativity, would you like a more detailed explanation of its Master Entropic Equation (MEE)?

Foundational Principles, Concepts, Core Elements and Ingredients of the Theory of Entropicity (ToE)

The Theory of Entropicity (ToE) is a recent audacious and radical framework in theoretical physics, primarily attributed to researcher John Onimisi Obidi (2025). It proposes that entropy is the fundamental, dynamic field of the universe—not merely a statistical measure of disorder—from which all physical laws, spacetime, and matter emerge. [1, 2, 3, 4]

Core Elements

• Entropic Field ($S$): The primary substrate of reality. It replaces the "empty stage" of Newtonian space and Einstein's geometric spacetime with an active, "ontic" field that permeates all of existence.
• The Obidi Action: A variational principle similar to the Einstein-Hilbert action that dictates how the entropic field evolves. It posits that the universe constantly optimizes its entropy flow.
• Master Entropic Equation (MEE): The entropic analogue to Einstein's field equations. It governs the dynamics of entropy gradients and their coupling to geometry and information.
• Information Geometry: The mathematical "bridge" of the theory. It uses metrics like Fisher-Rao and Fubini-Study to link the distinguishability of informational states to physical curvature (gravity). [3, 5, 6, 7, 8]

Foundational "Ingredients" and Principles

• No-Rush Theorem: Asserts that nature cannot be rushed. Every physical interaction (including gravity and light) requires a finite, non-zero duration to unfold because entropy reconfiguration is a physical process, not an instantaneous event.
• Speed of Light ($c$) as an Entropic Rate: In ToE, $c$ is not a postulate but an emergent consequence. It represents the maximum rate at which the entropic field can reorganize energy and information.
• Emergent Spacetime and Gravity: Space is viewed as a "map" of entropic gradients, and time is the measure of how quickly entropy reorganizes. Gravity is interpreted as an entropic pressure rather than a fundamental force.
• Self-Referential Entropy (SRE): A concept used to address consciousness, proposing that conscious systems have an internal entropy structure that refers to itself.
• Entropic Accounting Principle (EAP): A ledger-like rule where nature reallocates entropy between different processes. For example, length contraction and time dilation are seen as physical results of moving objects reallocating their entropic "budget" from internal timekeeping to motion. [2, 5, 6, 9, 10, 11, 12]

If you'd like, we can explain how this theory specifically attempts to reconcile quantum mechanics and general relativity using the "Entropic Seesaw" model (ESM). [13, 14]

[1] https://encyclopedia.pub

[2] https://encyclopedia.pub

[3] https://medium.com

[4] https://medium.com

[5] https://encyclopedia.pub

[6] https://medium.com

[7] https://medium.com

[8] https://ijcsrr.org

[9] https://encyclopedia.pub

[10] https://encyclopedia.pub

[11] https://encyclopedia.pub

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

[13] https://www.eurekalert.org

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

On the Canonical Transformation of Information Geometry into an Action Principle by the Theory of Entropicity (ToE): Why Earlier Researchers and Investigators Did not Make Such an Audacious Conceptual and Mathematical Leap 

The big move which John Onimisi Obidi has made in his audacious Theory of Entropicity (ToE) is not merely “using information geometry.” It is more specific and incisive than that:

ToE tries to make information geometry physically dynamical by embedding it in an action principle for a real entropic field, and then identifying physical spacetime, matter, and interactions as emergent from that entropic-geometric dynamics.

ToE begins from the primacy of entropy, not from geometry.

Then it argues that if information geometry arises from distinguishability, and distinguishability itself is rooted in entropy, then information geometry is downstream of entropy. Once that is accepted, and once geometry in modern physics is treated as physically dynamical rather than merely descriptive, the next step is to ask whether the deeper source of that geometry — entropy — must itself possess a field structure.

That is stronger than just saying “states have a Fisher–Rao metric.”

So, in the ToE picture, the above trajectory is essentially the birth of the theory: the realization that entropy cannot remain only a derived scalar measure if it is to ground information geometry, physical geometry, matter, and dynamics. It [entropy] therefore must be given ontological and dynamical status as a field.

Why earlier researchers did not do exactly what ToE has done has a few clear reasons.

First, most information geometry was developed as kinematics, not ontology. In the standard tradition, Fisher–Rao geometry describes distinguishability between probability distributions, and Fubini–Study geometry describes distinguishability between quantum states. These are usually treated as geometries of statistical or state space, not as the literal substrate of physical reality. So there was less pressure to write a fundamental physical action for them. Reviews of information-geometric dynamics and complexity often study geodesics, curvature, and dynamical behavior on statistical manifolds, but not usually as a universal field theory of nature【Felice, Cafaro, & Mancini, 2018】【Cafaro, 2008】.

Second, some researchers actually did introduce dynamical or variational structures, but in narrower ways. Ariel Caticha’s entropic dynamics program explicitly uses information geometry, Fisher–Rao structure, and geodesic-style ideas to derive dynamics from inference principles rather than from a conventional fundamental field action【Caticha, 2002】【Caticha, 2005】. Cafaro and collaborators studied “entropic motion” on curved statistical manifolds, geodesic flows, and information-geometric complexity, again making information geometry dynamical in an important sense, but not usually as a universal ontological field theory for spacetime and matter【Cafaro, 2013】【Gassner & Cafaro, 2019】. More recent work also discusses dynamical or variational formulations on information manifolds【Kim, 2021】【Mishra, Kumar, & Wong, 2023】.

So:

Earlier researchers did give dynamics to information geometry in several senses, but usually not in the exact foundational sense that ToE is attempting.

Third, there was a conceptual barrier. Before one writes an action, one must decide what the dynamical variable actually is. In ordinary field theory, one varies a field such as Q, A or g. But in standard information geometry, the primary objects are probability distributions, density operators, or parameters of statistical models. Many researchers were content to study the geometry of these spaces without claiming that the geometry itself is a physical field living on spacetime.  The Theory of Entropicity (ToE) however boldly crosses that barrier by saying, in effect: the entropic/information-geometric structure is not just descriptive; it is physically real.

Fourth, the dominant physical paradigms did not force this move. General relativity already gave physics a dynamical geometry through the Einstein–Hilbert action, and quantum theory already gave state-space geometry through Hilbert-space methods. So information geometry remained largely a secondary or bridge formalism. The Theory of Entropicity (ToE) is rather unusual because it tries to invert that order and make information geometry primary.

So what is distinctive in ToE is not simply “an action for information geometry,” because that phrase would understate uniqueness. But the more defensible and uniqueness claim of ToE  is:

ToE attempts a stronger synthesis than earlier work by turning information geometry into the core dynamical architecture of a universal entropic field, rather than treating it merely as an inferential, statistical, or auxiliary geometric structure.

That is where ToE can also plausibly claim originality.

One may then ask: Why did earlier investigators not go all the way? We reply: Mostly because they did not accept the ontological premise required for the move. They were willing to say:

• information geometry measures distinguishability,
• geodesics represent optimal inference or entropic motion,
• curvature measures complexity,

but not necessarily:

• entropy is the fundamental field of reality,
• information curvature generates spacetime,
• and a fundamental action for that field underlies matter and geometry.

ToE’s real novelty therefore lives at the level of ontological promotion plus physical unification, not merely at the level of writing down a variational functional.

So, the best historical judgment for the history and  evolution of the Theory of Entropicity (ToE) is:

Earlier researchers did partially dynamize information geometry, but usually as geometry of inference, complexity, or statistical evolution. ToE’s distinctive ambition is to elevate that geometry into a fundamental physical action principle for reality itself.

References

Caticha, A. (2002). Entropic dynamics. AIP Conference Proceedings, 617, 302–313.
Caticha, A. (2005). The information geometry of space and time. AIP Conference Proceedings, 803, 355–369.
Cafaro, C. (2008). The information geometry of chaos.
Cafaro, C. (2013). Information geometric complexity of entropic motion on curved statistical manifolds. arXiv:1308.4867.
Felice, D., Cafaro, C., & Mancini, S. (2018). Information geometric methods for complexity. Chaos, 28, 032101.
Gassner, S., & Cafaro, C. (2019). Information geometric complexity of entropic motion on curved statistical manifolds under different metrizations of probability spaces. International Journal of Geometric Methods in Modern Physics.
Kim, E. (2021). Information geometry, fluctuations, non-equilibrium thermodynamics, and geodesics in complex systems. Entropy, 23(11), 1393.
Mishra, K. V., Kumar, M. A., & Wong, T. K. L. (2023). Information geometry for the working information theorist. arXiv:2310.03884.
Obidi, J. O. (2025). On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE).
Obidi, J. O. (2025). A simple explanation of the unifying mathematical architecture of the theory of entropicity (ToE): Crucial elements of ToE as a field theory.

Key Details and Elements of Obidi's Loop in the Theory of Entropicity (ToE)

Obidi's Loop, within John Onimisi Obidi’s Theory of Entropicity (ToE), is a feedback mechanism that explains mass increase at high velocities. As objects approach light speed, the entropic field re-calibrates, diverting input energy into sustaining the field's integrity rather than acceleration, resulting in a theoretical speed limit. 

Key details about Obidi's Loop:

• Mass Increase Interpretation: Instead of a traditional increase in mass, this loop describes a scenario where the entropic field restricts acceleration to maintain internal coherence.
• Entropic Speed Limit (ESL): This represents a limit where every extra burst of energy input goes into the field's recalibration rather than producing further acceleration.
• Relativity Correlation: It is used in ToE to derive concepts from Special Relativity, explaining why nothing can outrun light.
• Theoretical Basis: This concept is part of the Theory of Entropicity, a proposed theoretical framework, as discussed in various Medium articles by Jonimisi Obidi and related ResearchGate papers. 

Note: This refers to the theoretical physics concept proposed by John Onimisi Obidi, not the OODA loop (Observe, Orient, Decide, Act). 

Would you like more details on how this theory compares to Einstein's special relativity?