The Theory of Entropicity (ToE) Derives and Explains Mass Increase, Time Dilation and Length Contraction in Einstein’s Theory of Relativity (ToR): ToE Applies Logical Entropic Concepts and Principles to Verify Einstein’s Relativity

The Theory of Entropicity (ToE) redefines entropy as the fundamental field and causal substrate of physical reality rather than a statistical byproduct of disorder. In this framework, entropy is treated as a continuous, dynamic field whose gradients generate motion, gravitation, time, and information flow. Central to the theory is the Obidi Action, a variational principle from which the Master Entropic Equation, Entropic Geodesics, and the Entropy Potential Equation emerge. By integrating Fisher–Rao and Fubini–Study metrics through the Amari–Čencov alpha-connection, ToE establishes a rigorous information-geometric foundation for entropy-driven dynamics. At its core, ToE reformulates the speed of light as the maximum rate of entropic rearrangement, deriving relativistic effects as consequences of finite entropy propagation. The No-Rush Theorem enforces a universal lower bound on causal intervals, while the Vuli–Ndlela Integral, an entropy-weighted reformulation of Feynman’s path integral, introduces irreversibility and temporal asymmetry into quantum mechanics. Together, these constructs unify thermodynamics, relativity, and quantum theory within a single entropic continuum. This work further demonstrates that mass increase, time dilation, and length contraction—traditionally postulated in Einstein’s relativity—arise naturally from entropic invariants and conservation laws. The Entropic Resistance Principle, within the Entropic Resistance Field, coupled with the Entropic Accounting Principle, explains how entropy is redistributed between motion and timekeeping, yielding the entropic Lorentz factor and reproducing Einstein’s transformations without geometric postulates. In doing so, ToE provides a unified, conceptually transparent framework that extends beyond theoretical physics to guide optimization, efficiency, and reliability in applied systems.