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The Mpemba effect, an example of anomalous thermal relaxations, occurs when asystem prepared at a hot temperature overtakes an identical system prepared ata warm temperature and cools down faster to the environment's temperature. Westudy the Mpemba effect in Markov jump processes on linear reaction networks asa function of the relaxation dynamics. The dynamics are characterized by a loaddistribution factor introduced to control the transition rates in a manner thatobeys detailed balance. We provide analytical results and insights on when theMpemba effect happens in the unimolecular reactions of three species as afunction of the dynamics. In particular, we derive that the regions of theStrong Mpemba effect in cooling and heating are non-overlapping and that thereis, at most, a single Strong Mpemba temperature. Next, we illustrate ourresults on a Maxwell demon setup, where we show that one can utilize the strongvariant of the Mpemba effect to have shorter cycles of the Maxwell demondevice, leading to increased power output, and stable device operation, withoutsacrificing efficiency.

Effect of dynamics on anomalous thermal relaxations and information exchange