Progress of the Theory of Entropicity (ToE): Literature on Novel Derivations of Einstein's Relativistic Kinematics and General Relativity in Modern Theoretical Physics 

The Theory of Entropicity (ToE) emerges within a growing but still fragmented body of work exploring thermodynamic, informational, and entropic origins of relativistic physics. While several authors have proposed partial connections between entropy, spacetime geometry, and relativistic kinematics, none provide a unified, first‑principles derivation that treats entropy density, entropy conservation, and the entropic field as the fundamental substrate from which relativistic effects and spacetime structure emerge.

The ToE positions itself as the first framework to derive:

- relativistic kinematics  

- gravitational curvature  

- time dilation  

- length contraction  

- mass variation  

- and deviations when the speed of light \(c\) is not constant  

directly from entropic field dynamics rather than from postulated invariances or geometric axioms.

This places the ToE in dialogue with — but distinct from — several modern research threads.

Methodology of the Theory of Entropicity (ToE)

The ToE is built on three methodological pillars:

1. The Entropy Field

A continuous field \(S(x)\) defined over an underlying information‑geometric manifold.  

This field encodes:

- local entropy density  

- entropic gradients  

- entropic curvature  

- the directionality of time  

2. The Conservation Principle

A fundamental conservation law:

\[

\nabla\mu J^\muS = 0

\]

where \(J^\mu_S\) is the entropy current.  

This replaces the postulate of invariant light speed with a deeper invariant: entropy flow cannot be destroyed, only redistributed.

3. Entropy Density and Relativistic Effects

Relativistic kinematics arise as emergent constraints on how entropy can redistribute under motion.  

From this, the ToE derives:

- time dilation as reduced entropy‑update rate  

- length contraction as compression of entropic degrees of freedom  

- mass increase as entropic curvature density  

- relativistic momentum as resistance to entropy reconfiguration  

A key prediction of the ToE is that if the speed of light \(c\) varies, the relativistic transformations deform in a precise, entropically determined way — connecting naturally to modified kinematics literature but grounded in a single entropic principle.

References and Historical Context

The ToE builds upon and extends several partial precedents:

Thermodynamic and Entropic Approaches

- Livadiotis & McComas (2025) — thermodynamic origins of relativity  

- Parker & Jeynes (2021) — entropic Hamiltonian dynamics  

- Chirco, Liberati & Relancio (2022) — spacetime thermodynamics  

- Bianconi (2025) — gravity from entropy  

These works hint at thermodynamic underlying relativity, but none derive the full relativistic framework from a single entropic field.

Information Geometry

- Amari (2016) — foundational information geometry  

The ToE uses information geometry not as a mathematical tool but as the substrate from which spacetime emerges.

Deformed and Modified Kinematics

- Carmona et al. (2019)  

- Pfeifer & Relancio (2022)  

- Russo & Townsend (2009)  

- Sahoo (2016)  

These works explore modified Lorentz transformations and deformed relativistic kinematics, but they lack a unifying physical principle.  

The ToE provides that principle: entropic curvature.

Arrow of Time

- Carroll (2010) — thermodynamic arrow of time  

The ToE replaces the thermodynamic arrow with the entropic‑geometric arrow, derived from the monotonic increase of Fisher information.

The Obidi Contribution

- Obidi (2025–2026) — Theory of Entropicity  

Obidi’s work introduces:

- the Entropic Primacy Axiom  

- the Information‑Geometric Substrate Axiom  

- the Obidi Equivalence Principle (OEP):  

  spacetime is the macroscopic projection of the underlying information‑geometric manifold, with geometric curvature corresponding to entropic curvature.

This is the first framework to unify:

- entropy  

- information geometry  

- relativistic kinematics  

- gravitational curvature  

- and potential variations in \(c\)  

under a single, coherent principle.