Distribution of current in non-equilibrium diffusive systems and phase transitions

TL;DR

This paper investigates phase transitions in non-equilibrium diffusive systems, showing how density profiles change from constant to time-dependent depending on current deviations, supported by numerical data and physical analysis.

Contribution

It introduces a detailed analysis of phase transitions in diffusive lattice gases on a ring, connecting current deviations to stability of density profiles and extending previous results.

Findings

Identification of a phase transition between constant and time-dependent density profiles

Numerical confirmation of the phase transition

Physical understanding of large drift limit behavior

Abstract

We consider diffusive lattice gases on a ring and analyze the stability of their density profiles conditionally to a current deviation. Depending on the current, one observes a phase transition between a regime where the density remains constant and another regime where the density becomes time dependent. Numerical data confirm this phase transition. This time dependent profile persists in the large drift limit and allows one to understand on physical grounds the results obtained earlier for the totally asymmetric exclusion process on a ring.