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Prog. Theor. Phys. Vol. 57 No. 3 (1977) pp. 746-758
On the Thermodynamic Limit in Equilibrium and Non-Equilibrium Systems
Masuo Suzuki
Department of Physics, University of Tokyo, Tokyo 113
(Received July 13, 1976)
Abstract:
The existence of a thermodynamic limit in some equilibrium and non-equilibrium systems is rigorously proven for a set of commutable local operators. Some statements on the existence of the thermodynamic limit for more general situations of non-equilibrium systems are given on the basis of the well-known theorem for equilibrium systems by Griffiths, Robinson and Ruelle. Finally the relation between the existence of the thermodynamic limit and the extensivity of the probability distribution function of a macrovariable is also discussed.
URL :
http://ptp.ipap.jp/link?PTP/57/746/
DOI : 10.1143/PTP.57.746
References:
- M. Suzuki, Prog. Theor. Phys. 53 (1975), 1657[PTP].
- M. Suzuki, in Proceedings of the International Symposium on Mathematical Problems in Theoretical Physics (Kyoto, Jan 23 - 29 1975, Springer, edited by H. Araki, Lecture Notes in Physics 39).
- M. Suzuki, J. Stat. Phys. 14 (1976), 129.
- D. Ruelle, Statistical Mechanics: Rigorous Results(W. A. Benjamin, Inc., New York, 1969).
R. B. Griffiths, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Acad. Press, 1972).
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R. B. Griffiths, J. Math. Phys. 5 (1964), 1215[CrossRef].
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D. W. Robinson, Commun. Math. Phys. 6 (1967), 151[CrossRef];
ibid. 7 (1968), 337[CrossRef].
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M. E. Fisher, Phys. Rev. 124 (1961), 1061[APS].
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P. W. Kasteleyn, Physica 27 (1962), 1209[CrossRef];
J. Math. Phys. 4 (1963), 287[CrossRef].
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E. H. Lieb, J. Math. Phys. 8 (1967), 2339[CrossRef].
- M. Suzuki, Prog. Theor. Phys. 46 (1971), 1337[PTP].
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R. M. Wilcox, J. Math. Phys. 8 (1967), 962[CrossRef].
- D. N. Zubarev, Nonequilibrium Statistical Mechanics, translated by P. J. Schepherd (Consultants Bureau, New York, 1974).
- H. F. Trotter, Proc. Am. Math. Soc. 10 (1959), 545.
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M. Suzuki, Commun. Math. Phys. 51 (1976), 183, [CrossRef]and references cited therein.
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R. Kubo, K. Matsuo and K. Kitahara, J. Stat. Phys. 9 (1973), 51[CrossRef].
- M. Suzuki, Prog. Theor. Phys. 55 (1976), 383[PTP]; ibid. 55 (1976), 1064[PTP].
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M. Suzuki, Phys. Lett. A 56 (1976), 71[CrossRef]; Prog. Theor. Phys. 56 (1976), 77[PTP]; ibid. 56 (1976), 477[PTP]; ibid. 57 (1977), 380[PTP]; J. Stat. Phys. 16 (1977), Nos. 1 and 6; Physica (in press).
Citing Article(s) :
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Progress of Theoretical Physics Vol. 57 No. 1 (1977) pp. 54-66
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Thermodynamic Limit in Quantum Stochastic Process
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Progress of Theoretical Physics Vol. 78 No. 4 (1987) pp. 787-799
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The ST-Transformation Approach to Analytic Solutions of Quantum Systems. I
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Progress of Theoretical Physics Supplement No.64 (1978) pp. 402-424
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Scaling Theory of Transient Nonlinear Fluctuations and Formation of Macroscopic Order
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