Zon-Cohen singularity and negative inverse temperature in a trapped particle limit

TL;DR

This paper investigates the statistical properties of work and heat in a Brownian particle within a moving periodic potential, revealing a Zon-Cohen singularity linked to rare trajectories with negative inverse temperature.

Contribution

It introduces a boundary layer analysis to compute cumulant generating functions and biased distributions, elucidating the Zon-Cohen singularity in fluctuation theorems.

Findings

Identification of a Zon-Cohen singularity in the fluctuation theorem

Calculation of cumulant generating function using boundary layer analysis

Discovery of rare trajectories characterized by negative inverse temperature

Abstract

We study a Brownian particle on a moving periodic potential. We focus on the statistical properties of the work done by the potential and the heat dissipated by the particle. When the period and the depth of the potential are both large, by using a boundary layer analysis, we calculate a cumulant generating function and a biased distribution function. The result allows us to understand a Zon-Cohen singularity for an extended fluctuation theorem from a view point of rare trajectories characterized by a negative inverse temperature of the biased distribution function.