CIC-MGE: Critical Dynamics of Chaos and Entropy

This work presents the CIC–MGE framework, a unified theoretical model describingcritical transitions in nonequilibrium systems through the interaction betweencontrolled instability amplification (Induced Chaos with Containment) andentropic saturation constraints (Entropic Bottleneck). The framework integrates phase-space dynamics, entropic thresholds, and instabilitycriteria, demonstrating how structural emergence arises from the dynamic tensionbetween chaos-driven expansion and entropic compression. Numerical experiments illustrate the CIC→MGE cycle and its emergent behavior.The model is applicable across multiple scales, including cosmological structureformation, gravitational dynamics, and complex adaptive systems. The work provides observable signatures and dynamical metrics that enable empiricalinvestigation of critical transitions in complex systems.