Work fluctuations for a Brownian particle driven by a correlated external random force

TL;DR

This paper analyzes the work fluctuations of a Brownian particle driven by a correlated Ornstein-Uhlenbeck force, deriving large deviation functions and validating results through numerical simulations.

Contribution

It provides a detailed analytical study of work fluctuations under correlated external forces, including symmetry properties and asymptotic probability distributions.

Findings

Derived large deviation functions for work fluctuations

Confirmed analytical results with numerical simulations

Identified symmetry properties of the large deviation functions

Abstract

We have considered the underdamped motion of a Brownian particle in the presence of a correlated external random force. The force is modeled by an Ornstein-Uhlenbeck process. We investigate the fluctuations of the work done by the external force on the Brownian particle in a given time interval in the steady state. We calculate the large deviation functions as well as the complete asymptotic form of the probability density function of the performed work. We also discuss the symmetry properties of the large deviation functions for this system. Finally we perform numerical simulations and they are in a very good agreement with the analytic results.