Exactly solvable model of stochastic heat engine: Optimization of power, its fluctuations and efficiency

We investigate a stochastic heat engine based on an over-damped particle diffusing on the positive real axis in an externally driven time-periodic log-harmonic potential. The periodic driving is composed of two isothermal and two adiabatic branches. Within our specific setting we verify the recent universal results regarding efficiency at maximum power and discuss properties of the optimal protocol. Namely, we show that for certain fixed parameters the optimal protocol maximizes not only the output power but also the efficiency. Moreover, we calculate the variance of the output work and discuss the possibility to minimize fluctuations of the output power.

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