The Critical Coupling Law: Minimum Phase Transition Condition in Diffusion-Cohesion Dynamics

Based on our previously established ”Diffusion-Cohesion Dynamics” (DCD) theoretical framework [1, 2, 3, 4, 5, 6], this paper proposes and validates a new physical law: in diffusion-cohesion dynamical systems, the minimum coupling strength required to trigger discontinuous phase transitions follows the critical formula δmin≈ k/( √ D ·C), where k ≈ 0.9 is a normalization constant. This law has been validated through systematic scanning of 2,197 parameter points in the DCD-CyberLife artificial consciousness system, demonstrating universality from quantum to cosmic scales. We provide theoretical derivation from variational principles and establish connections with existing phase transition theory, information theory, and complex systems theory. This law provides a unified mathematical framework for understanding transition behaviors in complex systems.