Prog. Theor. Phys. Vol. 55 No. 2 (1976) pp. 383-399

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Statistical Mechanics of Non-Equilibrium Systems. II

— Extensivity, Fluctuation and Relaxation of Markoffian Macrovariables —

Masuo Suzuki

Department of Physics, University of Tokyo, Tokyo

(Received June 20, 1975)

Abstract:

Kubo's extensivity Ansatz is proved for Markoffian macrovariables by the help of the mean value theorem and Haar's lemma, together with a rigorous derivation of the asymptotic equations of the distribution function and generating function in the thermodynamic limit. The existence and uniqueness of the solutions of these equations are proved under some appropriate conditions. Complete and general solutions of them are obtained to give the solution of the Cauchy problems. Time-evolution equations of the most probable path, variance and cumulants of higher order are derived on the basis of the asymptotic equation of the generating function. It is shown that the generalized thermodynamic potential approaches the equilibrium solution with the passage of time. The convergence of the system size expansion is also discussed.

URL : http://ptp.ipap.jp/link?PTP/55/383/
DOI : 10.1143/PTP.55.383

References:

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There are simple misprints in Eq. (86) in Ref. 2).

Citing Article(s) :

Progress of Theoretical Physics Vol. 55 No. 4 (1976) pp. 1064-1081 :
Statistical Mechanics of Non-Equilibrium Systems. III

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Progress of Theoretical Physics Vol. 56 No. 1 (1976) pp. 77-94 :
Scaling Theory of Non-Equilibrium Systems near the Instability Point. I

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Progress of Theoretical Physics Vol. 56 No. 2 (1976) pp. 477-493 :
Scaling Theory of Non-Equilibrium Systems near the Instability Point. II

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Progress of Theoretical Physics Vol. 57 No. 2 (1977) pp. 380-392 :
Scaling Theory of Non-Equilibrium Systems near the Instability Point. III

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Progress of Theoretical Physics Vol. 57 No. 3 (1977) pp. 746-758 :
On the Thermodynamic Limit in Equilibrium and Non-Equilibrium Systems

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Progress of Theoretical Physics Vol. 58 No. 4 (1977) pp. 1127-1141 :
Langevin Type Equations in Nonequilibrium State

Hiroshi Furukawa
Progress of Theoretical Physics Supplement No.64 (1978) pp. 402-424 :
Scaling Theory of Transient Nonlinear Fluctuations and Formation of Macroscopic Order

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Progress of Theoretical Physics Supplement No.79 (1984) pp. 125-140 :
Fluctuation and Formation of Macroscopic Order in Non-Equilibrium Systems

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Progress of Theoretical Physics Supplement No.87 (1986) pp. 1-22 :
Skeletonization, Fluctuating Mean-Field Approximations and Coherent Anomalies in Critical Phenomena

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