The Entropic Unity of Nature - Linking Gravitation, Inertia, and Information from Quantum to Cosmic Scales

This paper explores the unifying role of entropy and information in the emergence of gravitation, inertia, and spacetime geometry. Building on Erik Verlinde’s entropic-screen formulation and related informational approaches to gravity, the Entropic Cosmological Model (ECM) is introduced as a geometric–informational framework in which gravitational dynamics evolve with cosmic entropy while inertial response remains invariant. ECM reproduces MOND-like behavior through entropic scaling of curvature, but is silent on mass resisting motion when acted upon by a force, thereby preserving F = ma across all regimes. A natural quantum nat—one unit of Shannon information provides invariant measures of entropic length, time, and mass, linking microscopic informational discreteness to macroscopic gravitational phenomena. The resulting hierarchy connects quantum-scale invariant quantities (ℏ, α) with cosmological evolution (G ∝ 1/RU), where RU is the expanding radius of the universe, through a simple cosmological equation of state, where fundamental constants are balanced by variable parameters— temperature, radius, mass and gravity—that change over the evolution of the universe. In this view, nothing physical enters from “outside” the universe; all matter, energy, space, and time arise internally as relational consequences of entropy. The only quantity that may cross the cosmic boundary is information itself—dimensionless, non-physical, and generative.