Work distribution function for a Brownian particle driven by a nonconservative force

TL;DR

This paper derives the work distribution function for a Brownian particle under a harmonic force and rotational torque, revealing a Gaussian form that does not obey the standard fluctuation theorem, using the Onsager-Machlup approach.

Contribution

It introduces a novel derivation of the work distribution for a nonconservatively driven Brownian particle using the Onsager-Machlup functional integral method.

Findings

Work distribution is Gaussian.

Distribution does not satisfy the conventional fluctuation theorem.

Entropy production rate is linked to the Lagrangian difference.

Abstract

We derive the distribution function of work performed by a harmonic force acting on a uniformly dragged Brownian particle subjected to a rotational torque. Following the Onsager and Machlup's functional integral approach, we obtain the transition probability of finding the Brownian particle at a particular position at time $t$ given that it started the journey from a specific location at an earlier time. The difference between the forward and the time-reversed form of the generalized Onsager-Machlup's Lagrangian is identified as the rate of medium entropy production which further helps us develop the stochastic thermodynamics formalism for our model. The probability distribution for the work done by the harmonic trap is evaluated for an equilibrium initial condition. Although this distribution has a Gaussian form, it is found that the distribution does not satisfy the conventional work fluctuation theorem.