Microscopic background of the Onsager-Casimir reciprocity relations

Journal Article · Sat Oct 01 00:00:00 EDT 1988 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01011545· OSTI ID:6027793

Titulaer, U M

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.

• Research Organization: Johannes Kepler Universitaet Linz (Austria)
• OSTI ID: 6027793
• Journal Information: J. Stat. Phys.; (United States), Vol. 53:1-2
• Country of Publication: United States
• Language: English

Related Subjects

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