4.7 Article

Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag

Journal

PHYSICAL REVIEW E
Volume 105, Issue 5, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.105.054140

Keywords

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Funding

  1. MCIN/AEI [PID2020-112936GB-I00, PGC2018-093998-B-I00]
  2. Junta de Extremadura (Spain) [IB20079, GR21014]
  3. ERDF A way of making Europe
  4. Spanish Ministerio de Ciencia, Innovacion y Universidades [FPU2018-3503]

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In this paper, the Mpemba effect is investigated in a molecular gas through analytic and numerical methods. The study reveals a nonmutual correspondence between the thermal and entropic Mpemba effects, and suggests that the relaxation process of the thermal Mpemba effect is better described by the relaxation of the local equilibrium distribution.
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.

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