Anomalous thermal relaxation in unimolecular chemical reactions

Thermal quenching is the process of rapidly cooling or heating a physical system. A curious phenomenon that sometimes occurs during such rapid thermal relaxations is the so-called Mpemba effect. It is the phenomenon where a system prepared at a hot temperature "overtakes" an identical system prepared at a warm temperature and cools down faster to be in equilibrium with a cold environment. There is also the analogous phenomenon in heating, and it is called the inverse Mpemba effect. Here we study the Mpemba effect and its inverse in unimolecular chemical reactions as a function of the chemical reaction rates and the system's energies. We observe both effects in unimolecular chemical reactions of three or more species and provide analytical results. We generalize some of the results to N-species chemical reactions. Potential applications of our work could lead to optimized protocols for obtaining chemical products and better characterizations of biochemical pathways.