Space-time Phase Transitions in Driven Kinetically Constrained Lattice Models

TL;DR

This paper explores space-time phase transitions in driven kinetically constrained models (KCMs), revealing a first-order transition between dynamical phases distinguished by entropy production, extending understanding of glassy dynamics to non-equilibrium systems.

Contribution

It demonstrates that driven KCMs exhibit a space-time phase transition analogous to undriven systems, characterized by entropy production, and introduces a mapping to modified forces for rare trajectory realizations.

Findings

Driven KCMs show a first-order space-time transition in entropy production.

Trajectories with rare entropy production can be mapped to systems with modified forces.

The transition separates phases of finite and vanishing activity.

Abstract

Kinetically constrained models (KCMs) have been used to study and understand the origin of glassy dynamics. Despite having trivial thermodynamic properties, their dynamics slows down dramatically at low temperatures while displaying dynamical heterogeneity as seen in glass forming supercooled liquids. This dynamics has its origin in an ergodic-nonergodic first-order phase transition between phases of distinct dynamical "activity". This is a "space-time" transition as it corresponds to a singular change in ensembles of trajectories of the dynamics rather than ensembles of configurations. Here we extend these ideas to driven glassy systems by considering KCMs driven into non-equilibrium steady states through non-conservative forces. By classifying trajectories through their entropy production we prove that driven KCMs also display an analogous first-order space-time transition between dynamical phases of finite and vanishing entropy production. We also discuss how trajectories with rare values of entropy production can be realized as typical trajectories of a mapped system with modified forces.