# Dynamical aspects of spontaneous symmetry breaking in driven flow with exclusion

## TL;DR

This paper numerically investigates a two-lane asymmetric exclusion process, revealing how spontaneous symmetry breaking and state transitions depend on boundary conditions and indicating proximity to critical points.

## Contribution

It introduces a detailed analysis of symmetry-breaking dynamics and flip statistics in a two-lane exclusion model, extending domain-wall theory to understand density reversals.

## Key findings

- Identification of flip time distributions and their relation to criticality.
- Evidence of precursor events before symmetry-breaking flips.
- Adaptation of domain-wall theory to model density reversals.

## Abstract

We present a numerical study of a two-lane version of the stochastic non-equilibrium model known as the totally asymmetric simple exclusion process. For such a system with open boundaries, and suitably chosen values of externally-imposed particle injection ($\alpha$) and ejection ($\beta$) rates, spontaneous symmetry breaking can occur. We investigate the statistics and internal structure of the stochastically-induced transitions, or "flips", which occur between opposite broken-symmetry states as the system evolves in time. From the distribution of time intervals separating successive flips, we show that the evolution of the associated characteristic times against externally-imposed rates yields information regarding the proximity to a critical point in parameter space. On short time scales, we probe for the possible existence of precursor events to a flip between opposite broken-symmetry states. We study an adaptation of domain-wall theory to mimic the density reversal process associated with a flip.