Work fluctuations for a Brownian particle in a harmonic trap with fluctuating locations

TL;DR

This paper analyzes the work fluctuations of a Brownian particle in a harmonic trap with a stochastically fluctuating location, deriving the work distribution and examining fluctuation theorem validity.

Contribution

It provides the first detailed theoretical analysis of work fluctuations for a Brownian particle in a dynamically modulated harmonic trap, including large deviation functions.

Findings

Derived the asymptotic form of the work distribution.

Confirmed the fluctuation theorem applicability.

Numerical results agree with theoretical predictions.

Abstract

We consider a Brownian particle in a harmonic trap. The location of the trap is modulated according to an Ornstein-Uhlenbeck process. We investigate the fluctuation of the work done by the modulated trap on the Brownian particle in a given time interval in the steady state. We compute the large deviation as well as the complete asymptotic form of the probability density function of the work done. The theoretical asymptotic forms of the probability density function are in very good agreement with the numerics. We also discuss the validity of the fluctuation theorem for this system.