Current large deviations for partially asymmetric particle systems on a ring

TL;DR

This paper investigates large deviations of particle current in one-dimensional stochastic systems with periodic boundaries, extending previous results to more general systems and identifying a dynamic phase transition.

Contribution

It generalizes large deviation results to partially asymmetric systems with various current-density relations, including zero-range and inclusion processes.

Findings

Predicted large deviation rate functions for full current fluctuation range.

Supported predictions with simulation results using cloning algorithms.

Identified a dynamic phase transition in partially asymmetric zero-range processes.

Abstract

We study large deviations for the current of one-dimensional stochastic particle systems with periodic boundary conditions. Following a recent approach based on an earlier result by Jensen and Varadhan, we compare several candidates for atypical currents to travelling wave density profiles, which correspond to non-entropic weak solutions of the hyperbolic scaling limit of the process. We generalize previous results to partially asymmetric systems and systems with convex as well as concave current-density relations, including zero-range and inclusion processes. We provide predictions for the large deviation rate function covering the full range of current fluctuations using heuristic arguments, and support them by simulation results using cloning algorithms wherever they are computationally accessible. For partially asymmetric zero-range processes we identify an interesting dynamic phase transition between different strategies for atypical currents, which is of a generic nature and expected to apply to a large class of particle systems on a ring.