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

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 are 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 is 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.