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A colloidal particle embedded in a fluid can be used as a microscopic heatengine by means of a sequence of cyclic transformations imposed by an opticaltrap. We investigate a model for the operation of such kind of Brownian engineswhen the surrounding medium is viscoelastic, which endows the particle dynamicswith memory friction. We analyze the effect of the relaxation time of the fluidon the performance of the colloidal engine under finite-time Stirling cycles.We find that, due to the frequency-dependence of the friction in viscoelasticfluids, the mean power delivered by the engine and its efficiency can be highlyenhanced as compared to those in a viscous environment with the same zero-shearviscosity. In addition, with increasing fluid relaxation time the interval ofcycle times at which positive power output can be delivered by the enginebroadens. Our results reveal the importance of the transient behavior of thefriction experienced by a Brownian heat engine in a complex fluid, which cannotbe neglected when driven by thermodynamic cycles of finite duration.

Work extraction and performance of colloidal heat engines in viscoelastic baths