Dynamical criticality in open systems: non-perturbative physics, microscopic origin and direct observation

TL;DR

This paper investigates the microscopic origins and macroscopic phenomena of dynamical phase transitions in driven diffusive systems, revealing symmetry-breaking, non-convex large deviation functions, and degeneracy of microscopic states through theoretical analysis and simulations.

Contribution

It provides a comprehensive analysis of dynamical phase transitions in open systems, linking microscopic degeneracies to macroscopic symmetry-breaking phenomena.

Findings

Identification of a $ ext{Z}_2$ symmetry-breaking transition

Observation of non-convex large deviation functions below criticality

Confirmation of theoretical predictions through extensive simulations

Abstract

Driven diffusive systems may undergo phase transitions to sustain atypical values of the current. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such fluctuations. Here we shed light on both the macroscopic large deviation properties and the microscopic origin of such spontaneous symmetry breaking in the open weakly asymmetric exclusion process. By studying the joint fluctuations of the current and a collective order parameter, we uncover the full dynamical phase diagram for arbitrary boundary driving, which is reminiscent of a $\mathbb{Z}_2$ symmetry-breaking transition. The associated joint large deviation function becomes non-convex below the critical point, where a Maxwell-like violation of the additivity principle is observed. At the microscopic level, the dynamical phase transition is linked to an emerging degeneracy of the ground state of the microscopic generator, from which the optimal trajectories in the symmetry-broken phase follow. In addition, we observe this new symmetry-breaking phenomenon in extensive rare-event simulations, confirming our macroscopic and microscopic results.