# Generic Dynamical Phase Transition in One-Dimensional Bulk-Driven Lattice Gases with Exclusion

## TL;DR

This paper demonstrates a universal dynamical phase transition in one-dimensional bulk-driven exclusion processes, showing different scaling behaviors for high and low current deviations, and extends analysis methods to more general models.

## Contribution

It generalizes the understanding of dynamical phase transitions in exclusion processes by including spatial inhomogeneities and short-range interactions, beyond exactly solvable models.

## Key findings

- High current deviations scale extensively with system size.
- Low current deviations are independent of system size.
- Transition relates to pushing current beyond hydrodynamic limits.

## Abstract

Dynamical phase transitions are crucial features of the fluctuations of statistical systems, corresponding to boundaries between qualitatively different mechanisms of maintaining unlikely values of dynamical observables over long periods of time. They manifest themselves in the form of non-analyticities in the large deviation function of those observables. In this paper, we look at bulk-driven exclusion processes with open boundaries. It is known that the standard asymmetric simple exclusion process exhibits a dynamical phase transition in the large deviations of the current of particles flowing through it. That phase transition has been described thanks to specific calculation methods relying on the model being exactly solvable, but more general methods have also been used to describe the extreme large deviations of that current, far from the phase transition. We extend those methods to a large class of models based on the ASEP, where we add arbitrary spatial inhomogeneities in the rates and short-range potentials between the particles. We show that, as for the regular ASEP, the large deviation function of the current scales differently with the size of the system if one considers very high or very low currents, pointing to the existence of a dynamical phase transition between those two regimes: high current large deviations are extensive in the system size, and the typical states associated to them are Coulomb gases, which are correlated ; low current large deviations do not depend on the system size, and the typical states associated to them are anti-shocks, consistently with a hydrodynamic behaviour. Finally, we illustrate our results numerically on a simple example, and we interpret the transition in terms of the current pushing beyond its maximal hydrodynamic value, as well as relate it to the appearance of Tracy-Widom distributions in the relaxation statistics of such models.