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Title: Microscopic background of the Onsager-Casimir reciprocity relations

Abstract

It has been known for some time that small deviations from the Onsager-Casimir symmetry relations are introduced when one passes from a given description of a system to a less detailed one by adiabatic elimination of fast variables. Exact validity is preserved, however, for a slightly modified form of these relations. In this paper the question is considered whether this modified Onsager symmetry is also preserved by the transition from a microscopic to a mesoscopic description, the step that introduces manifest irreversibility into the equations of motion. This question is examined in detail for a system of a few heavy oscillators coupled to a bath, a model discussed in a recent paper by van Kampen. The modified Onsager symmetry survives the transition to an irreversible description via the dense spectrum approximation. This is shown explicitly by inspection of the results obtained by van Kampen; some arguments favoring a more general validity are also briefly discussed.

Authors:
Publication Date:
Research Org.:
Johannes Kepler Universitaet Linz (Austria)
OSTI Identifier:
6027793
Resource Type:
Journal Article
Journal Name:
J. Stat. Phys.; (United States)
Additional Journal Information:
Journal Volume: 53:1-2
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HARMONIC OSCILLATOR MODELS; IRREVERSIBLE PROCESSES; ONSAGER RELATIONS; SYMMETRY; ADIABATIC PROCESSES; BOLTZMANN-VLASOV EQUATION; CREATION OPERATORS; EIGENVECTORS; HAMILTONIANS; HILBERT SPACE; INVARIANCE PRINCIPLES; MANY-BODY PROBLEM; PARTICLE MODELS; STATISTICAL MECHANICS; THERMODYNAMICS; TIME DEPENDENCE; TRANSFORMATIONS; BANACH SPACE; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MATHEMATICAL SPACE; MECHANICS; PARTIAL DIFFERENTIAL EQUATIONS; QUANTUM OPERATORS; SPACE; 657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics

Citation Formats

Titulaer, U M. Microscopic background of the Onsager-Casimir reciprocity relations. United States: N. p., 1988. Web. doi:10.1007/BF01011545.
Titulaer, U M. Microscopic background of the Onsager-Casimir reciprocity relations. United States. https://doi.org/10.1007/BF01011545
Titulaer, U M. 1988. "Microscopic background of the Onsager-Casimir reciprocity relations". United States. https://doi.org/10.1007/BF01011545.
@article{osti_6027793,
title = {Microscopic background of the Onsager-Casimir reciprocity relations},
author = {Titulaer, U M},
abstractNote = {It has been known for some time that small deviations from the Onsager-Casimir symmetry relations are introduced when one passes from a given description of a system to a less detailed one by adiabatic elimination of fast variables. Exact validity is preserved, however, for a slightly modified form of these relations. In this paper the question is considered whether this modified Onsager symmetry is also preserved by the transition from a microscopic to a mesoscopic description, the step that introduces manifest irreversibility into the equations of motion. This question is examined in detail for a system of a few heavy oscillators coupled to a bath, a model discussed in a recent paper by van Kampen. The modified Onsager symmetry survives the transition to an irreversible description via the dense spectrum approximation. This is shown explicitly by inspection of the results obtained by van Kampen; some arguments favoring a more general validity are also briefly discussed.},
doi = {10.1007/BF01011545},
url = {https://www.osti.gov/biblio/6027793}, journal = {J. Stat. Phys.; (United States)},
number = ,
volume = 53:1-2,
place = {United States},
year = {Sat Oct 01 00:00:00 EDT 1988},
month = {Sat Oct 01 00:00:00 EDT 1988}
}