Current large deviations for driven periodic diffusions

TL;DR

This paper analyzes the large deviations of current fluctuations in driven periodic diffusions, using Fourier-Bloch decomposition to derive large deviation functions and construct effective processes, providing insights into fluctuation regimes and bounds.

Contribution

It introduces a Fourier-Bloch decomposition approach to derive large deviation functions and construct effective processes for driven diffusions on the circle.

Findings

Derived large deviation functions for current fluctuations.

Constructed effective Markov processes explaining fluctuation regimes.

Compared upper bounds with entropic bounds and analyzed low-noise limits.

Abstract

We study the large deviations of the time-integrated current for a driven diffusion on the circle, often used as a model of nonequilibrium systems. We obtain the large deviation functions describing the current fluctuations using a Fourier-Bloch decomposition of the so-called tilted generator and also construct from this decomposition the effective (biased, auxiliary or driven) Markov process describing the diffusion as current fluctuations are observed in time. This effective process provides a clear physical explanation of the various fluctuation regimes observed. It is used here to obtain an upper bound on the current large deviation function, which we compare to a recently-derived entropic bound, and to study the low-noise limit of large deviations.