Mpemba effect in molecular gases under nonlinear drag

Abstract

We look into the Mpemba effect---the initially hotter sample cools sooner---in a molecular gas with nonlinear viscous drag. Specifically, the gas particles interact among them via elastic collisions and also with a background fluid at equilibrium. Thus, within the framework of kinetic theory, our gas is described by an Enskog--Fokker--Planck equation. The analysis is carried out in the first Sonine approximation, in which the evolution of the temperature is coupled to that of the excess kurtosis. This coupling leads to the emergence of the Mpemba effect, which is observed in an early stage of the relaxation and when the initial temperatures of the two samples are close enough. This allows for the development of a simple theory, linearizing the temperature evolution around a reference temperature---namely the initial temperature closer to the asymptotic equilibrium value. The linear theory provides a semiquantitative description of the effect, including expressions for the crossover time and the maximum temperature difference. We also discuss the limitations of our linearized theory.