Lower current large deviations for zero-range processes on a ring

TL;DR

This paper investigates the lower large deviations of current in zero-range processes on a ring, revealing a dynamic transition from wave-like to condensed profiles, supported by theoretical analysis and numerical simulations.

Contribution

It introduces a novel dynamic transition in large deviations for zero-range processes, characterizing the rate function with detailed examples and extending methods from exclusion processes.

Findings

Identification of a dynamic transition in current fluctuations

Characterization of the rate function for various jump rates

Numerical validation using cloning algorithms

Abstract

We study lower large deviations for the current of totally asymmetric zero-range processes on a ring with concave current-density relation. We use an approach by Jensen and Varadhan which has previously been applied to exclusion processes, to realize current fluctuations by travelling wave density profiles corresponding to non-entropic weak solutions of the hyperbolic scaling limit of the process. We further establish a dynamic transition, where large deviations of the current below a certain value are no longer typically attained by non-entropic weak solutions, but by condensed profiles, where a non-zero fraction of all the particles accumulates on a single fixed lattice site. This leads to a general characterization of the rate function, which is illustrated by providing detailed results for four generic examples of jump rates, including constant rates, decreasing rates, unbounded sublinear rates and asymptotically linear rates. Our results on the dynamic transition are supported by numerical simulations using a cloning algorithm.