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

This work presents a theoretical framework for 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 within a Kuramoto-like formalism. 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 of relational entropy while the global entropy remains conserved. This mechanism provides a physically motivated perspective on how highly coherent, effectively low-entropy macroscopic states can emerge dynamically from underlying chaotic microscopic interactions in closed systems.