The microscopic background of thermodynamics
type: Item
instance of: scholarly article
title: The microscopic background of thermodynamics
zbMATH Open document ID: 0599.76004
author: B. George
published in: Journal of Non-Equilibrium Thermodynamics
publication date: 1985-01-01T00:00:00Z
review text: In this report two modes of description of a macroscopic system are contrasted: (1) by thermodynamics, using balance equations, and constitutive laws; (2) by quantum mechanics, in terms of observables, represented by ''selfadjoint operators on a separable Hilbert space'', a statistical operator, and canonical equations of motion. The classical dilemma resulting from the fact that these descriptions are strictly contradictory - as expressed by the cliché that thermodynamics is deterministic and irreversible while quantum mechanics is statistical and reversible - is discussed at some length. It is suggested that the dilemma can be solved and that a ''microscopic background of thermodynamics'' can be provided by quantum mechanics if only two (or three) postulates are added to its usual axioms. These postulates delimit the class of macroscopic observables and statistical operators. They correspond to a particular assumption of ''coarse graining''. Developing this idea further, the author indicates how, for special systems, the microscopic description (based on quantum mechanics or classical [statistical] particle mechanics) can be reduced, first to kinetic description in terms of a Boltzmann type equation of motion, and finally, by obtaining so called normal solutions of the Chapman-Enskog type, to a generalized thermodynamic description in terms of a sequence of (generalized) balance equations. As an example the case of dilute gas of ''Brownian particles'' governed by the Fokker-Planck equation is treated. No details of calculations and results are given in this report, but a full list of references is provided.
Mathematics Subject Classification ID: 76A02
Mathematics Subject Classification ID: 82B30
Mathematics Subject Classification ID: 81P05
Mathematics Subject Classification ID: 76P05
zbMATH DE Number: 3968101
zbMATH Keywords: macroscopic system
zbMATH Keywords: balance equations
zbMATH Keywords: constitutive laws
zbMATH Keywords: statistical operator
zbMATH Keywords: canonical equations of motion
zbMATH Keywords: microscopic background of thermodynamics
zbMATH Keywords: coarse graining
zbMATH Keywords: kinetic description
zbMATH Keywords: Boltzmann type equation of motion
zbMATH Keywords: normal solutions of the Chapman-Enskog type
zbMATH Keywords: Fokker- Planck equation
MaRDI profile type: Publication
full work available at URL: jnet.1985.10.4.315
OpenAlex ID: W4250664265
cites work: A master equation for gases
cites work: Proper and normal solutions of the Fokker-Planck equation
DOI: 10.1515/JNET.1985.10.4.315
description: scientific article; zbMATH DE number 3968101