Anomalous thermal relaxation dynamics in a Maxwell demon setup

The Mpemba effect, an example of anomalous thermal relaxations, occurs when a system prepared at a hot temperature overtakes an identical system prepared at a warm temperature and cools down faster to the environment's temperature. Typically, the studies have focused on finding initial conditions (temperatures) that allow such a relaxation shortcut. Here, we study the role of the dynamics in the Mpemba effect. Moreover, we focus on the Strong Mpemba effect, which occurs when there is a jump in the relaxation time of the system. Our paradigms are three- and four-level Markov jump processes, whose relaxation dynamics we vary in a way that conserves detailed balance. In particular, for the three-level system, we show that the phase space regions with the Strong Mpemba effect in cooling and heating are non-overlapping and that there is, at most, a single Strong Mpemba temperature. In addition, as an application, we illustrate our results on a Maxwell demon setup. We show that one can utilize the Strong Mpemba effect to obtain shorter cycles of the Maxwell demon device, leading to increased power output and stable device operation. This can be done without sacrificing the efficiency of the device, thus creating efficient erasers and heat engines.