Cyclic active refrigerators

Thermodynamic cycles are idealized processes that can convert heat into work or produce heat flow against a temperature gradient with the input of work. They remain an active area of research in modern stochastic thermodynamics. In particular, cyclic active heat engines have been shown to display a rich phenomenology, such as ``violations'' of the Carnot bound on efficiency and an improved performance in comparison to their passive counterparts. We introduce the concept of cyclic active refrigerators using a previously derived second law for cyclic active systems. We show that for cyclic active refrigerators, a naive definition of the coefficient of performance can exceed the bound set by the standard second law for passive refrigerators. We also show that cyclic active systems can behave like a Maxwell's demon, with heat flowing from the cold to the hot reservoir without any work input. Beyond this phase, cyclic active systems can enter a hybrid phase, functioning as both a heat engine and a refrigerator simultaneously. Our results are obtained with two models that involve active Brownian particles, a simpler one that allows for analytical results and a more realistic one that is analyzed through numerical simulations.