Stochastic efficiency of an isothermal work-to-work converter engine

We investigate the efficiency of an isothermal Brownian work-to-work converter engine, composed of a Brownian particle coupled to a heat bath at a constant temperature. The system is maintained out of equilibrium by using two external time-dependent stochastic Gaussian forces, where one is called load force and the other is called drive force. Work done by these two forces are stochastic quantities. The efficiency of this small engine is defined as the ratio of stochastic work done against load force to stochastic work done by the drive force. The probability density function as well as large deviation function of the stochastic efficiency are studied analytically and verified by numerical simulations.