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.
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References
L. Onsager,Phys. Rev. 37:405 (1931);38:2265 (1931).
H. B. G. Casimir,Rev. Mod. Phys. 17:343 (1945).
J. A. McLennan,Phys. Rev. A 10:1272 (1974).
U. Geigenmüller, U. M. Titulaer, and B. U. Felderhof,Physica 119A:53 (1983).
G. F. Hubmer and U. M. Titulaer,J. Stat. Phys. 49:331 (1987).
G. F. Hubmer and U. M. Titulaer,J. Stat. Phys. 50:913 (1988).
N. G. van Kampen,Physica 147A:165 (1987).
B. U. Felderhof and U. M. Titulaer,Physica 100A:563 (1980).
U. M. Titulaer and B. U. Felderhof,Physica 100A:573 (1980).
T. Kato,Perturbation Theory for Linear Operators, 2nd ed. (Springer, Berlin, 1976).
N. G. van Kampen,Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981), Chapter V.
N. G. van Kampen,Dan. Mat. Fys. Medd. 26(15) (1951).
H. Mori,Prog. Theor. Phys. 34:423 (1965); R. Zwanzig,Lectures in Theoretical Physics, Vol. 3 (Wiley, New York, 1961).
U. M. Titulaer,Physica 100A:234 (1980).
U. Geigenmüller, U. M. Titulaer, and B. U. Felderhof,Physica 119A:41 (1983).
C. Bloch,Nucl. Phys. 6:329 (1958).
U. Geigenmüller, U. M. Titulaer, and B. U. Felderhof,Physica 120A:635 (1983).
P. Ullersma,Physica 32:27, 56, 74, 90 (1966).
P. Ullersma and J. A. Tjon,Physica 71:294 (1974).
J. Machta and I. Oppenheim,Physica 112A:361 (1982).
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This paper is dedicated to Prof. Nico van Kampen.
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Titulaer, U.M. On the microscopic background of the Onsager-Casimir reciprocity relations. J Stat Phys 53, 61–75 (1988). https://doi.org/10.1007/BF01011545
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DOI: https://doi.org/10.1007/BF01011545