On the Foundations of the Theory of Entropicity (ToE): Conceptual and Mathematical Formulation Pillars, Key Theorems, and Comparisons with Other Theories 

The Theory of Entropicity (ToE), originated by John Onimisi Obidi in 2025, is a theoretical physics framework that proposes entropy is not a statistical measure of disorder, but the fundamental, dynamic field of reality from which space, time, and gravity emerge. [1, 2]

Core Conceptual Foundations

• Entropy as an Ontic Field: Unlike standard physics where entropy is a secondary property, ToE treats it as a primary, continuous scalar field ($S(x,t)$) that permeates all existence.
• Emergent Spacetime: Space is viewed as a "map" of entropic gradients, while time is the directional flux or "heartbeat" of the field as it reconfigures.
• Speed of Light ($c$) as an Entropic Rate: The universal constant $c$ is reinterpreted as the maximum rate at which the entropic field can reorganize energy and information.
• Gravity as Entropic Pressure: Gravity is explained as a system's tendency to move toward regions that maximize entropic flow, rather than being a fundamental force. [2, 3, 4, 5, 6, 7]

Foundational Mathematical Pillars

• The Obidi Action: A universal variational principle used to derive physical laws. It unifies classical and quantum information geometries (Fisher–Rao and Fubini–Study metrics).
• The Master Entropic Equation (MEE): Also known as the Obidi Field Equations (OFE), this is the entropic analogue to Einstein's field equations, governing how entropy gradients couple to geometry and matter.
• Information Geometry: The theory uses the Amari–Čencov $\alpha$-connection to link informational divergence (uncertainty) to physical curvature. [4, 8, 9, 10, 11]

Key Theorems

1. The No-Rush Theorem (NRT): States that no physical process can occur instantaneously; every interaction requires a finite duration for the entropic field to redistribute.
2. The No-Go Theorem (NGT): Asserts that once a stable, distinguishable state is realized, the process is fundamentally irreversible, providing a geometric basis for wavefunction collapse.
3. Obidi Curvature Invariant (OCI): Sets a universal lower bound (defined as $\ln 2$) on the entropic cost required to distinguish two states. [3, 12, 13, 14, 15]

Comparisons to Other Theories

• vs. Entropic Gravity (Verlinde): While Verlinde sees gravity as an emergent force, ToE goes further by replacing the spacetime fabric entirely with an ontic entropic field.
• vs. General Relativity: ToE claims to be a superset of Einstein's relativity, reinterpreting effects like time dilation and mass increase as manifestations of entropic resistance (ERP) to field reconfiguration. [3, 8, 10]

Are you interested in how the Theory of Entropicity (ToE) reinterprets specific quantum phenomena like entanglement or the Elitzur–Vaidman bomb tester?

[1] https://papers.ssrn.com

[2] https://medium.com

[3] https://medium.com

[4] https://encyclopedia.pub

[5] https://medium.com

[6] https://medium.com

[7] https://medium.com

[8] https://medium.com

[9] https://www.linkedin.com

[10] https://medium.com

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

[12] https://encyclopedia.pub

[13] https://encyclopedia.pub

[14] https://encyclopedia.pub

[15] https://encyclopedia.pub

Appendix: Extra Matter 

The Theory of Entropicity (ToE), formulated by John Onimisi Obidi in 2025, proposes that entropy is not a mere measure of disorder, but the fundamental physical field and causal substrate of reality. It suggests that spacetime, gravity, mass, energy, and information flow emerge from the dynamics of this underlying entropy field. 

Key Foundations of the Theory of Entropicity:

• The Entropic Field: Space is not empty, but a dense field of informational states where entropy acts as a primary, continuous field that shapes physical reality.
• Entropic Gravity: Gravity is reinterpreted as "entropic pressure"—a result of gradients in the field rather than spacetime curvature.
• Emergent Time: Time is not a fundamental dimension, but rather a representation of the rate at which entropy changes.
• The Obidi Action: A mathematical foundation using variational principles to derive physical laws, where the universe evolves by optimizing entropic cost and flow.
• Core Theorems: Includes the No-Go Theorem (NGT) (no physical process can be stable and reversible simultaneously) and the No-Rush Theorem (NRT) (a lower bound on the duration of interactions, prohibiting instantaneous physical processes).
• Entropic Seesaw Model: Explains quantum entanglement and wave function collapse as connected entities along an "entropic bar". 

The Theory of Entropicity aims to unify quantum mechanics, general relativity, and thermodynamics through this single, information-based, and post-Einsteinian framework. 

• Official Archive/GitHub: Theory of Entropicity (ToE)
• Read the Primary Formulation (Medium): The Theory of Entropicity (ToE): A New Framework for Understanding Reality