Exact distribution for work and stochastic efficiency of an isothermal machine

Abstract

We consider an isothermal machine composed of two Brownian particles (say particle A and B) connected by a harmonic spring. A constant load is attached to particle A, and the particle B is trapped in a harmonic confinement whose minimum is dragged with a constant velocity. We obtain the distribution for work done on particle A and particle B. The transient fluctuation theorem for these quantities is tested in the weak coupling limit for both small and large observation times. Moreover, we show that the transient fluctuation theorem for the total work done on both particles is satisfied. Furthermore, we compute the stochastic efficiency which is the ratio of the work done against the load force on particle A and the work done on particle B of this machine. The probability density function for stochastic efficiency is computed for all time. Numerical simulations are also done to verify the analytical results.