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Loosely speaking, the Mpemba effect appears when hotter systems cool sooneror, in a more abstract way, when systems further from equilibrium relax faster.In this paper, we investigate the Mpemba effect in a molecular gas withnonlinear drag, both analytically (by employing the tools of kinetic theory)and numerically (direct simulation Monte Carlo of the kinetic equation andevent-driven molecular dynamics). The analysis is carried out via twoalternative routes, recently considered in the literature: first, the kineticor thermal route, in which the Mpemba effect is characterized by the crossingof the evolution curves of the kinetic temperature (average kinetic energy),and, second, the stochastic thermodynamics or entropic route, in which theMpemba effect is characterized by the crossing of the distance to equilibriumin probability space. In general, a nonmutual correspondence between thethermal and entropic Mpemba effects is found, i.e., there may appear thethermal effect without its entropic counterpart or vice versa. Furthermore, anontrivial overshoot with respect to equilibrium of the thermal relaxationmakes it necessary to revise the usual definition of the thermal Mpemba effect,which is shown to be better described in terms of the relaxation of the localequilibrium distribution. Our theoretical framework, which involves an extendedSonine approximation in which not only the excess kurtosis but also the sixthcumulant is retained, gives an excellent account of the behavior observed insimulations.

Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag