Work fluctuations for a harmonic oscillator driven by an external random force

TL;DR

This paper analyzes the work fluctuations of a harmonic oscillator driven by an external Gaussian random force, deriving exact large deviation functions and exploring the validity of fluctuation theorems under different conditions.

Contribution

It provides the exact large deviation function and asymptotic forms of the work distribution for a driven harmonic oscillator, revealing conditions for fluctuation theorem validity.

Findings

Work distribution is non-Gaussian.

Steady state fluctuation theorem holds only if the variance ratio is less than 1/3.

Transient fluctuation theorem holds asymptotically for all variance ratios.

Abstract

The fluctuations of the work done by an external Gaussian random force on a harmonic oscillator that is also in contact with a thermal bath is studied. We have obtained the exact large deviation function as well as the complete asymptotic forms of the probability density function. The distribution of the work done are found to be non-Gaussian. The steady state fluctuation theorem holds only if the ratio of the variances, of the external random forcing and the thermal noise respectively, is less than 1/3. On the other hand, the transient fluctuation theorem holds (asymptotically) for all the values of that ratio. The theoretical asymptotic forms of the probability density function are in very good agreement with the numerics as well as with an experiment.