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.

💡 Research Summary

The paper introduces the concept of cyclic active refrigerators, extending the framework of stochastic thermodynamics to systems that are driven by internal activity (e.g., bacteria‑powered colloidal particles). Building on a recently derived second‑law inequality for cyclic active systems, the authors show that the usual definition of the coefficient of performance (COP) can be surpassed when the active contribution is taken into account.

The theoretical backbone starts from a Markov master equation with periodic transition rates. Temperature, energy levels, and an “affinity” (F(t)) (which quantifies the activity) are introduced. The generalized detailed‑balance condition links transition rates to these thermodynamic parameters. Heat exchanged with the cold and hot reservoirs, (Q_c) and (Q_h), and the work per cycle, (W), are defined in the usual way, leading to a refined first law (W = Q_c + Q_h) that excludes the direct dissipation associated with the activity.

The novelty lies in the extra term (I) appearing in the second‑law expression for active cycles: \