Anomalous thermal relaxation and the Mpemba effect of Langevin particles

The Mpemba effect is an anomalous relaxation process in which a system starting at a hot temperature cools down faster than an identical system starting at an initially lower temperature when both are coupled to an even colder bath. The effect has been observed in water, clathrate hydrates, magnetic alloys, and driven granular gases. We search for an analogous to Mpemba phenomenon for the case of a Langevin particle diffusing and advecting on a potential energy landscape. The particle is diffusing with a diffusion constant, that corresponds to a temperature that is lower than specified by the initial condition. We study the Mpemba effect, or non-monotonic thermal relaxation, as a function of parameters specifying the potential landscape.