Anomalous thermal relaxation in unimolecular chemical reactions and connections to symmetries of the system

The Mpemba effect is a prime example of anomalous thermal relaxations. Imagine two identical systems are prepared at different temperatures, and each is separately coupled to an infinite bath with yet another temperature. If the process of relaxing to the environment were quasistatic, the system with a smaller temperature difference would asymptotically equilibrate faster. However, things might not be so for other kinds of relaxation dynamics. The system, which initially has a larger mismatch between its and the environment's temperature, can, in some cases, equilibrate sooner. When this happens, we call it the Mpemba effect.

We study the Mpemba effect in unimolecular chemical reactions as a function of the chemical reaction rates. We observe the Mpemba effect in unimolecular chemical reactions of three or more reactants. We provide analytical results and insights on when the effect happens, connecting the occurrence of the Mpemba effect to the topological features and symmetries of the system.