Colloquia

Rapid cooling or heating of a physical system can lead to unusual thermal relaxation phenomena. A prime example of anomalous thermal relaxation is the Mpemba effect. The phenomenon occurs when a system prepared at a hot temperature overtakes an identical system prepared at a warm temperature and equilibrates faster to the cold environment. A similar effect exists in heating. Comparing two identical physical systems in their equilibration, we would expect that the system with a smaller mismatch between its and the environment’s temperature will thermalize faster – yet it is not always the case. I will present theoretical results on the Mpemba effect in over-damped Langevin dynamics and Markov jump processes. I will link the Mpemba effect’s occurrence with the physical systems’ properties and dynamics. In particular, I will derive the necessary conditions for the Mpemba effect in the small diffusion limit of one-dimensional over-damped Langevin dynamics on a double-well potential. Our results show the strong Mpemba effect occurs when the probability of being in a well at initial and bath temperature match, which agrees with experiments. I also derive the conditions for the weak Mpemba effect and express the conditions for both effects in terms of mean first passage time. Next, I will provide analytical results and insights on when the Mpemba effect happens in Markov jump processes as a function of the dynamics. Markov jump processes that obey detailed balance (microscopic reversibility) relax to equilibrium. However, the detailed balance only determines the ratio of the backward and forward rates, not their magnitudes. The magnitudes specify the dynamics. I will introduce a control parameter to vary the dynamics and show when we see the effect as a function of the dynamics. Lastly, I will explore the connections between the Mpemba effect and optimal transport. This material is based upon work supported by the National Science Foundation under Grant No. DMR-1944539.