Micro-reversibility and thermalization with collisional baths

Jannik Ehrich, Massimiliano Esposito, Felipe Barra and Juan M.R. Parrondo

Physica A: Statistical Mechanics and its Applications, 2020, vol. 552, issue C

Abstract: Micro-reversibility plays a central role in thermodynamics and statistical mechanics. It is used to prove that systems in contact with a thermal bath relax to canonical ensembles. However, a problem arises when trying to reproduce this proof for classical and quantum collisional baths, i.e. particles at equilibrium interacting with a localized system via collisions. In particular, micro-reversibility appears to be broken and some models do not thermalize when interacting with Maxwellian particles. We clarify these issues by showing that micro-reversibility needs the invariance of evolution equations under time reversal plus the conservation of phase space volume in classical and semiclassical scenarios. Consequently, all canonical variables must be considered to ensure thermalization. This includes the position of the incident particles which maps their Maxwellian distribution to the effusion distribution. Finally, we show an example of seemingly plausible collision rules that do not conserve phase-space volume, and consequently violate the second law.

Keywords: Liouville’s theorem; Detailed balance; Equilibration; Repeated interactions; Effusion (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:552:y:2020:i:c:s0378437119312257

DOI: 10.1016/j.physa.2019.122108

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