A stochastic Stirling engine powered by an active particle

Abstract We investigate a model of a stochastic engine operating cyclically in a viscous fluid at constant temperature, where the working substance consists of an overdamped Brownian particle confined by a harmonic potential, which is elastically coupled to an active particle that is part of the environment. Stirling-like cycles are implemented by time-periodic changes of the active particle speed and the confining potential. We find two operation regimes of this engine, which are governed by the relative magnitudes of the persistence time of the active particle, the characteristic time of its interaction with the working substance, and the viscous relaxation time of the latter. First, in an optimal performance regime, the quasistatic efficiency is very close to a second-law-like upper bound, also exhibiting the broadest intervals of finite cycle times for work production as a motor with the highest output powers, which occurs when the viscous relaxation time of the working substance is the dominant time-scale. Second, a suboptimal regime arises when either the persistence time of the active particle or the characteristic interaction time is comparable or larger than the viscous relaxation time, in which the engine performance is hindered.