A Brownian cyclic engine operating in a viscoelastic active suspension

We investigate a model for Stirling-like engine consisting of passive Brownian particle confined by harmonic potential and interacting with suspension active particles that self-propel in viscous solvent, which cyclically operates under isothermal conditions means temporal variations the trap stiffness self-propulsion speed particles. derive an effective stochastic equation motion trapped particle, includes friction memory kernel as well thermal fluctuating forces due to its coupling suspension, from we analytically compute efficiency quasi-static limit. find that, on average, is capable produce mechanical work depends interplay between different time-scales system, where general effect ensuing viscoelasticity reduce engine, compared case system instantaneous friction. Nevertheless, there are regions parameters space such effects negligible performance thus effectively behaving contact inert bath working at two temperatures related propulsion