Hyperuniform systems are maximally irreversible

Abstract

Hyperuniform systems, defined by the anomalous suppression of large-scale density fluctuations, are a paradigm of non-equilibrium self-assembly. While mechanisms underlying the self-assembly of hyperuniform states have been widely studied, the energetics of this process remain unexplored. This raises a fundamental question: what is the energetic cost of self-assembling a hyperuniform system? Here, we address this question across several noisy particle systems drawn from soft matter and machine learning, in which hyperuniformity can be induced by tuning noise correlations. Despite their distinct microscopic dynamics, we uncover a universal behavior across all systems: hyperuniform states are maximally irreversible, as quantified by the entropy production rate. Further, we develop a path integral formulation of the entropy production rate directly from the microscopic dynamics, which explains our observations. Our work establishes a direct link between emergent long-range structure and time irreversibility and opens a new avenue of probing the energetic cost of hyperuniform self-assembly, ubiquitous across physics, biology, and materials science.