Dynamical phase transitions in one-dimensional hard-particle systems

TL;DR

This paper investigates phase transitions in a one-dimensional hard-particle system under biased dynamical activity, revealing phase separation at low activity and hyperuniform states at high activity, with differences between constant volume and pressure ensembles.

Contribution

It introduces a detailed analysis of large deviations in dynamical activity for 1D hard-particle systems, highlighting ensemble differences and the emergence of distinct phases.

Findings

Phase separation occurs at low activity levels.

Hyperuniform states form at high activity levels.

Ensemble differences affect density fluctuation probabilities.

Abstract

We analyse a one-dimensional model of hard particles, within ensembles of trajectories that are conditioned (or biased) to atypical values of the time-averaged dynamical activity. We analyse two phenomena that are associated with these large deviations of the activity: phase separation (at low activity) and the formation of hyperuniform states (at high activity). We consider a version of the model which operates at constant volume, and a version at constant pressure. In these non-equilibrium systems, differences arise between the two ensembles, because of the extra freedom available to the constant-pressure system, which can change its total density. We discuss the relationships between different ensembles, mechanical equilibrium, and the probability cost of rare density fluctuations.