Entropic Gravity as an Evolutionary Process: A Unification with the Genesis-Integration Principle

The Genesis-Integration Principle (GIP) provides a universal mathematical framework describing evolutionary dynamics across diverse systems. This paper extends GIP to cosmological evolution by integrating it with entropic gravity theory. Cosmic evolution is interpreted as an entropy-driven evolutionary process governed by information dynamics, aligning with GIP's established three-phase model: exponential growth, sigmoidal transition, and power-law stabilization. Clear mathematical connections between GIP and entropic gravity—specifically Verlinde's entropic gravity and Bekenstein-Hawking entropy—are established. Furthermore, this paper emphasizes how these evolutionary patterns cyclically recur throughout cosmic history, bridging the Big Bang with future cosmological states.