Work and heat distributions for a Brownian particle subjected to an oscillatory drive

TL;DR

This paper analyzes the work and heat distributions of a Brownian particle under oscillatory driving, revealing how these distributions evolve with frequency and their deviation from fluctuation theorems.

Contribution

It introduces a functional integral approach to derive work and heat distributions for a driven Brownian particle, highlighting frequency effects and distribution characteristics.

Findings

Work distribution width saturates at high frequency

Heat distribution is Gaussian for small fluctuations

Heat distribution generally violates the transient fluctuation theorem

Abstract

Using the Onsager-Machlup functional integral approach, we obtain the work distribution function and the distribution of the dissipated heat of a Brownian particle subjected to a confining harmonic potential and an oscillatory driving force. In the long time limit, the width of the work distribution function initially increases with the frequency of the driving force and finally saturates to a fixed value for large values of the angular frequency. Using the results from the work distribution part, we next obtain the distribution of the dissipated heat for the equilibrium initial condition. Using the method of steepest descent, we obtain a Gaussian distribution for small fluctuations in the large time limit. The distribution function, for a fixed time has been obtained numerically. It is shown that the heat distribution, in general, does not satisfy the transient fluctuation theorem.