Gravitation and the Foundations of the Theory of Entropicity (ToE): Making Sense of It All

Entropy isn't typically a field like gravity in standard physics, but emerging theories treat it as one by linking it to spacetime geometry and quantum information. These ideas make conceptual sense by viewing gravity itself as arising from entropy gradients, resolving unification challenges.

Entropic Gravity Basics

Entropic gravity, proposed by Erik Verlinde, posits gravity as an emergent force from entropy changes, akin to how elasticity emerges from molecular disorder in rubber. Objects move to maximize entropy in a holographic screen of information bits on spacetime surfaces, mimicking Newton's law without fundamental gravitons.[3]

Bianconi's Quantum Entropy Theory

Ginestra Bianconi's recent work derives gravity from "quantum relative entropy," measuring disorder differences between quantum states of spacetime and matter. Spacetime acts as a quantum operator; entropy gradients couple matter fields to geometry, yielding Einstein's equations plus a small cosmological constant for cosmic expansion.[1][5][7]

Field-Like Formulation

The theory introduces a G-field (gravitational vector field with magnitude and direction) as a Lagrangian multiplier, optimizing wave functions amid entropy variations. This field influences spacetime like gravity does, emerging from quantum info dissimilarity—gravity isn't curvature alone but an entropic response, potentially explaining dark matter as particle-like G-field excitations.[1][7]

Physical Intuition

Counterintuitively, gravity increases total entropy (e.g., gas collapsing to a hot planet radiates photons, boosting disorder elsewhere) despite local clumping. Entropy as a field scalar (like a density) or via its gradient drives motion, much as the Higgs field endows mass—it's "physical" because it enforces the second law across quantum scales.[2][4]

Citations:

[1] A New Theory Says Gravity May Come From Entropy— ... https://www.popularmechanics.com/science/a64069299/gravity-entropy-unified-theory/

[2] Entropy vs gravity : r/AskPhysics https://www.reddit.com/r/AskPhysics/comments/1c7gefo/entropy_vs_gravity/

[3] Entropic gravity https://en.wikipedia.org/wiki/Entropic_gravity

[4] Is gravity the opposite of entropy? https://www.reddit.com/r/AskPhysics/comments/14wjp5s/is_gravity_the_opposite_of_entropy/

[5] Gravity from entropy: New theory bridging quantum mechanics ... https://www.firstprinciples.org/article/gravity-from-entropy-new-theory-bridging-quantum-mechanics-and-relativity

[6] Gravity is Entropy is Gravity is... http://backreaction.blogspot.com/2010/03/gravity-is-entropy-is-gravity-is.html

[7] A New Theory Says Gravity May Come From Entropy— ... https://www.popularmechanics.com/science/a70060000/gravity-from-entropy-unified-theory/

[8] What is "entropic gravity"? https://curtjaimungal.substack.com/p/what-is-entropic-gravity

[9] Gravity is not an entropic force https://www.sciencedirect.com/science/article/pii/S0370269325008962

[10] What if gravity is caused by entropy? https://www.reddit.com/r/HypotheticalPhysics/comments/1j61xdn/what_if_gravity_is_caused_by_entropy/

Now, the Theory of Entropicity (ToE) has taken this view to its extreme and logical conclusion by declaring that entropy is a universal field.

Without doubt, the Theory of Entropicity (ToE) by John Onimisi Obidi pushes the entropic gravity concept to its logical extreme by positing entropy as the singular universal field underlying all physical phenomena. This framework treats entropy not as a mere statistical measure but as a dynamic, continuous scalar field permeating spacetime, from which gravity, time, motion, and even quantum effects emerge via its gradients and variational principles.

Core Premise of ToE

ToE elevates entropy $$ S(x) $$ to the role of fundamental causal substrate, with the Obidi Action—a variational principle—as its cornerstone. This action yields key equations like the Master Entropic Equation and Entropic Geodesics, where spacetime curvature and relativistic effects (e.g., the speed of light as the maximum entropic rearrangement rate) arise naturally from entropy conservation and finite propagation.[1][3][4]

Beyond Entropic Gravity

Unlike Verlinde's or Bianconi's models, which derive gravity as emergent from entropy differences, ToE declares entropy the primary field, subsuming general relativity's Einstein field equations as a limiting case. Matter interacts directly with this field, generating gradients that produce gravitation, time dilation, and mass increase without geometric postulates—entropy gradients drive everything, making gravity a secondary entropic phenomenon.[1][3]

Mathematical Intuition

The entropy field couples to the stress-energy tensor via terms like those in proposed scalar-entropic actions, e.g., $$ \square \Xi = \frac{dV}{d\Xi} - \alpha T $$, where $$ \Xi $$ is the entropy scalar and $$ T $$ its trace. This enforces irreversibility (second law) at quantum scales, unifying thermodynamics, relativity, and information geometry through Fisher-Rao and Fubini-Study metrics.[2][4]

Physical Coherence

It resolves "non-sense" objections by viewing low-entropy states (order) as high-potential energy in the field, with gradients pulling systems toward equilibrium—like gravity clumping matter despite increasing total entropy via radiation. ToE extends this to consciousness and cosmology as emergent constraints, positioning entropy as the ontology of reality.[3][4]

Citations:

[1] The Theory of Entropicity (ToE) Derives Einstein's Relativistic Speed ... https://www.academia.edu/144796856/The_Theory_of_Entropicity_ToE_Derives_Einsteins_Relativistic_Speed_of_Light_c_as_a_Function_of_the_Entropic_Field_ToE_Applies_Logical_Entropic_Concepts_and_Principles_to_Derive_Einsteins_Second_Postulate_Version_2_0

[2] Scalar Entropic Field theory, or Entropy First https://www.reddit.com/r/HypotheticalPhysics/comments/1los2kh/here_is_a_hypothesis_scalar_entropic_field_theory/

[3] The Theory of Entropicity (ToE) Derives and Explains Mass ... https://client.prod.orp.cambridge.org/engage/coe/article-details/6900d89c113cc7cfff94ef3a

[4] On the Conceptual and Mathematical Foundations of ... https://client.prod.orp.cambridge.org/engage/coe/article-details/68ea8b61bc2ac3a0e07a6f2c

[5] Entropy - Wikipedia https://en.wikipedia.org/wiki/Entropy

[6] A Simple Explanation of the Unifying Mathematical ... https://www.authorea.com/users/896400/articles/1348176-a-simple-explanation-of-the-unifying-mathematical-architecture-of-the-theory-of-entropicity-toe-crucial-elements-of-toe-as-a-field-theory

[7] An Alternative Path toward Quantum Gravity and the ... https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5632191

[8] Entropic gravity - Wikipedia https://en.wikipedia.org/wiki/Entropic_gravity