Macroscopic Coherence in Closed Nonlinear Lattices: Phase Synchronization and Effective Entropy Reduction

This work investigates the emergence of macroscopic coherence in closed nonlinear systems. We consider an abstract lattice of globally coupled nonlinear oscillators subject to stochastic fluctuations and analyze its dynamics using a Kuramoto-like framework. Despite the absence of an external thermal bath, we show that effective damping can arise from the coarse-graining of microscopic degrees of freedom into an emergent macroscopic collective variable. As the system undergoes a phase synchronization transition, the microscopic degrees of freedom become phase-aligned, leading to a significant reduction in relational entropy while the global entropy remains conserved. This framework suggests a possible mechanism for the dynamical generation of effectively low-entropy macroscopic states from chaotic microscopic dynamics in closed systems, with potential relevance to emergent classical behavior.