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Prog. Theor. Phys. Vol. 56 No. 3 (1976) pp. 754-772

Reduction of Variables and Processes in Macrodynamics

Hirokazu Fujisaka and Hazime Mori

Department of Physics, Kyushu University, Fukuoka 812

(Received February 21, 1976)

Abstract:

It is shown that the projection-operator method in the Heisenberg picture in non-equilibrium statistical mechanics can be extended to formulate the reduction of macrovariables in non-Hamiltonian systems far from thermal equilibrium whose time evolution is described by either stochastic or deterministic equations. Mori's scaling method for the reduction of processes is used to single out the long-time behavior characteristic of the relevant set of macrovariables. As illustrations, Haken's model for the coupling between a system and reservoirs and Edelstein's model for biochemical reactions near a critical point are studied from this new point of view. Thus it is shown that the Ginzburg-Landau type nonlinear equations for the fluctuations of the critical modes hold if α= β, and this method is more useful than the reductive-perturbation method.

URL : http://ptp.ipap.jp/link?PTP/56/754/
DOI : 10.1143/PTP.56.754

[ Full Text PDF : FREE ACCESS (1321K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 56 No. 4 (1976) pp. 1073-1092 :

   Statistical-Mechanical Theory of the Boltzmann Equation and Fluctuations in µ Space

   Michio Tokuyama and Hazime Mori

2. Progress of Theoretical Physics Vol. 58 No. 4 (1977) pp. 1127-1141 :

   Langevin Type Equations in Nonequilibrium State

   Hiroshi Furukawa

3. Progress of Theoretical Physics Vol. 62 No. 1 (1979) pp. 70-90 :

   Study of Langevin Type Equations by Means of a New Projection Operator Method in Nonequilibrium States

   Hiroshi Furukawa

4. Progress of Theoretical Physics Vol. 63 No. 6 (1980) pp. 1865-1884 :

   Contraction of State Variables in Non-Equilibrium Open Systems. I

   Hazime Mori, Terumitsu Morita and Kazuko T. Mashiyama

5. Progress of Theoretical Physics Vol. 64 No. 2 (1980) pp. 500-521 :

   Contraction of State Variables in Non-Equilibrium Open Systems. II

   Terumitsu Morita, Hazime Mori and Kazuko T. Mashiyama

6. Progress of Theoretical Physics Supplement No.64 (1978) pp. 50-64 :

   Scalng for the Space-Time Coarse Graining and Kinetic Equations

   Hazime Mori, Michio Tokuyama and Terumitsu Morita

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