Large deviation function for the entropy production: Optimal trajectory and role of fluctuations

TL;DR

This paper investigates the large deviation function for entropy production in driven systems, comparing two theoretical approaches and revealing how optimal trajectories influence the function's shape, including the formation of a kink.

Contribution

It provides a detailed comparison of Donsker-Varadhan and Freidlin-Wentzell theories in analyzing entropy production, highlighting the role of optimal trajectories and fluctuation effects.

Findings

Wings of the large deviation function are dominated by single optimal trajectories.

The joining of branches at zero entropy production causes a non-differentiable kink.

Many trajectories around zero entropy production smear out the kink.

Abstract

We study the large deviation function for the entropy production rate in two driven one-dimensional systems: the asymmetric random walk on a discrete lattice and Brownian motion in a continuous periodic potential. We compare two approaches: the Donsker-Varadhan theory and the Freidlin-Wentzell theory. We show that the wings of the large deviation function are dominated by a single optimal trajectory: either in forward (positive rate) or in backward direction (negative rate). The joining of both branches at zero entropy production implies a non-differentiability and thus the appearance of a "kink". However, around zero entropy production many trajectories contribute and thus the kink is smeared out.