Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag

TL;DR

This study explores the Mpemba effect in a molecular gas with nonlinear drag, revealing differences between thermal and entropic relaxation processes through analytical and numerical methods.

Contribution

It introduces a comprehensive kinetic theory framework including higher-order cumulants to analyze the Mpemba effect in nonlinear drag gases, highlighting nonmutual effects.

Findings

Thermal and entropic Mpemba effects can occur independently.

Overshoot phenomena require redefining the thermal Mpemba effect.

The extended Sonine approximation accurately predicts simulation results.

Abstract

Loosely speaking, the Mpemba effect appears when hotter systems cool sooner or, in a more abstract way, when systems further from equilibrium relax faster. In this paper, we investigate the Mpemba effect in a molecular gas with nonlinear drag, both analytically (by employing the tools of kinetic theory) and numerically (direct simulation Monte Carlo of the kinetic equation and event-driven molecular dynamics). The analysis is carried out via two alternative routes, recently considered in the literature: first, the kinetic or thermal route, in which the Mpemba effect is characterized by the crossing of the evolution curves of the kinetic temperature (average kinetic energy), and, second, the stochastic thermodynamics or entropic route, in which the Mpemba effect is characterized by the crossing of the distance to equilibrium in probability space. In general, a nonmutual correspondence between the thermal and entropic Mpemba effects is found, i.e., there may appear the thermal effect without its entropic counterpart or vice versa. Furthermore, a nontrivial overshoot with respect to equilibrium of the thermal relaxation makes 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 local equilibrium distribution. Our theoretical framework, which involves an extended Sonine approximation in which not only the excess kurtosis but also the sixth cumulant is retained, gives an excellent account of the behavior observed in simulations.