Resolving entropy contributions in nonequilibrium transitions

TL;DR

This paper introduces a functional to quantify entropy contributions from microscopic correlations, applicable in and out of equilibrium, enabling the identification of governing degrees of freedom during dynamic transitions.

Contribution

It presents a novel formalism for entropy estimation based on pair correlations, applicable to systems with broken translational invariance and varying particle numbers.

Findings

Captured the crossover from crystalline to disordered hyperuniform states in emulsions.

Identified cross-correlations between droplet positions and sizes as key to hyperuniformity.

Provided insights into entropy estimation and transition characterization in disordered systems.

Abstract

We derive a functional for the entropy contributed by any microscopic degrees of freedom as arising from their measurable pair correlations. Applicable both in and out of equilibrium, this functional yields the maximum entropy which a system can have given a certain correlation function. When applied to different correlations, the method allows us to identify the degrees of freedom governing a certain physical regime, thus capturing and characterizing dynamic transitions. The formalism applies also to systems whose translational invariance is broken by external forces and whose number of particles may vary. We apply it to experimental results for jammed bidisperse emulsions, capturing the crossover of this nonequilibrium system from crystalline to disordered hyperuniform structures as a function of mixture composition. We discover that the cross-correlations between the positions and sizes of droplets in the emulsion play the central role in the formation of the disordered hyperuniform states. We discuss implications of the approach for entropy estimation out of equilibrium and for characterizing transitions in disordered systems.