Effect of dynamics on anomalous thermal relaxations and information exchange

The Mpemba effect, an example of anomalous thermal relaxation, occurs when a system prepared at a higher temperature overtakes an identical system prepared at a lower temperature and cools down faster to the environment's temperature. We explore the Mpemba effect within Markov jump processes on linear reaction networks and study the effect as a function of the relaxation dynamics. The dynamics are characterized by a load distribution factor introduced to modulate the transition rates in a manner that obeys detailed balance. We analytically diagonalize the dynamical generator of three-species unimolecular reactions and, through graphic exploration of parameters, identify the regimes in which the Mpemba effect occurs. In particular, we find that the regions of the strong variant of the Mpemba effect, known as the strong Mpemba effect, in cooling and heating are nonoverlapping and that there is, at most, a single strong Mpemba temperature. Furthermore, we demonstrate our findings using a Maxwell demon setup. In this context, we demonstrate that leveraging the strong Mpemba effect can lead to shorter cycles of the Maxwell demon device, thereby enhancing power output without compromising the stability of device operation or its efficiency.