A stochastic Stirling engine powered by an active particle

Abstract: We investigate a model of a stochastic engine operating cyclically at constant bath temperature, which consists of an overdamped Brownian harmonic oscillator that plays the role of working substance and is elastically coupled to an active particle. Stirling-like cycles are implemented by time-periodic changes of the active particle speed and the potential confining the oscillator. By analyzing its quasistatic and finite-time performance, we distinguish two regimes, which are determined by the relative magnitudes of the persistence time of active particle, the characteristic time of the elastic interaction, and the viscous relaxation time of the working substance. In the quasistatic limit, we derive analytic expressions for the average output work, the mean absorbed heat, and the efficiency, which explicitly involve the ratios of such three time-scales. For sufficiently large finite cycles, the different quantities characterizing the engine performance converge to their quasistatic values. For shorter cycles, the efficiencies are systematically lower, but with positive mean output powers that exhibit a maximum as a function of the cycle duration if the corresponding quasistatic mean work is positive. For sufficiently short cycles or if the quasistatic work is zero, the engine behaves at finite-time as a heat pump with negative power and efficiency.