Fluctuations and correlations in weakly asymmetric simple exclusion on a ring subject to an atypical current

TL;DR

This paper analyzes the correlation structure and fluctuation dynamics of a weakly asymmetric simple exclusion process on a ring under atypical current conditions, revealing long-range correlations and detailed fluctuation behavior.

Contribution

It provides a detailed computation of correlations and fluctuation dynamics in current-biased exclusion processes, extending previous heuristic results and addressing parameter restrictions.

Findings

Long-range correlations induced by current bias

Characterization of fluctuation dynamics around optimal density

Recovery of heuristic correlation results

Abstract

We consider the weakly asymmetric simple exclusion process on a ring, driven out of equilibrium by tilting the dynamics so as to enforce a macroscopic current of particles on a large time interval. In this current-biased dynamics, the tilt by the current makes the dynamics non-local, non homogeneous and induces long-range correlations. We compute the correlation structure in the large time, large size limit for a certain range of asymmetry and current strength, recovering heuristic results of Bodineau et al. arXiv:0807.2394. In addition, in this range of parameters, we characterise the full dynamics of fluctuations around the optimal density profile in the current-biased dynamics. The key ingredient at the microscopic scale is a precise relative entropy estimate at the level of correlations. We also discuss how to remove the (technical) restriction on the range of parameters.