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      Mpemba-like effect in a molecular binary mixture in contact with a thermal reservoir

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          Abstract

          The Mpemba effect occurs when two samples at different initial temperatures evolve in such a way that the temperatures cross each other during the relaxation towards equilibrium. In this paper we show the emergence of a Mpemba-like effect in a molecular binary mixture in contact with a thermal reservoir (bath). The interaction between the gaseous particles of the mixture and the thermal reservoir is modeled via a viscous drag force plus a stochastic Langevin-like term. The presence of the external bath couples the time evolution of the total and partial temperatures of each component allowing the appearance of the Mpemba phenomenon, even when the initial temperature differences are of the same order of the temperatures themselves. Analytical results are obtained by considering multitemperature Maxwellian approximations for the velocity distribution functions of each component. The theoretical analysis is carried out for initial states close to and far away (large Mpemba-like effect) from equilibrium. The former situation allows us to develop a simple theory where the time evolution equation for the temperature is linearized around its asymptotic equilibrium solution. This linear theory provides an expression for the crossover time. We also provide a qualitative description of the large Mpemba effect. Our theoretical results agree very well with computer simulations obtained by numerically solving the Enskog kinetic equation by means of the direct simulation Monte Carlo method and by performing molecular dynamics simulations.

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          Author and article information

          Journal
          27 October 2020
          Article
          2010.14215
          c5b5baf2-6aee-4a9a-839c-1eb0cb2b89bc

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          12 pages; 5 figures
          cond-mat.stat-mech

          Condensed matter
          Condensed matter

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