Non Markovian Mpemba Effect in Chemical Reaction Networks.

The Mpemba effect is a prime example of anomalous thermal relaxation, when a hot system relaxes to thermal equilibrium before an identical cold system when both are coupled to the same even colder bath. This effect has gained a lot of recent attention and has both experimentally and theoretically been studied in classical and quantum systems. However, most of the recent works have been focused on understanding the Mpemba effect in Markovian settings, that is, systems without memory. In this talk, we study the presence and behavior of the Mpemba effect in non-Markovian chemical reactions. We show how the memory present in the system affects its relaxation and make connections with previous works involving optimal transport protocols in linear reaction networks and overdamped Langevin dynamics. We use an effective chemical master equation to model the molecular memory in a discrete network setting and compare the effective description to Monte Carlo simulations and numerical solutions. We will also briefly comment on how non-Markovian noise affects the Langevin dynamics and the nature of the Mpemba effect.