Mpemba effect in molecular fluids: a kinetic theory approach

We investigate the emergence of the Mpemba effect in a molecular fluid with nonlinear viscous drag. Thus, fluid particles undergo non-linear Brownian motion and the fluid is described by an Enskog--Fokker--Planck equation within the framework of kinetic theory. The Mpemba effect emerges as a consequence of the coupling of the evolution equations of the temperature and the excess kurtosis. The smallness of the latter makes it possible to develop an approximate theory that gives a quantitative account of the conditions for the Mpemba effect to come about. Moreover, we discuss how the system has to be previously aged to observe the Mpemba effect. Other memory phenomena, like the Kovacs hump, can also be described with a similar approach.