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Prog. Theor. Phys. Vol. 63 No. 6 (1980) pp. 1865-1884

[ Full Text PDF : FREE ACCESS (1436K) ]

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

Hazime Mori, Terumitsu Morita and Kazuko T. Mashiyama

Department of Physics, Kyushu University, Fukuoka 812

(Received September 4, 1979)

Abstract:

A projector elimination of irrelevant macrovariables is formulated for dissipative systems far from thermal equilibrium whose time evolution is described by autonomous deterministic equations with appropriate initial ensembles. Reduced equations of motion for relevant macrovariables and the corresponding master equation are obtained in terms of the fluctuating forces generated by the elimination. For a complete set of slowly-varying variables, the second-order terms in their expansion in powers of a slowness parameter lead to a Langevin and a Fokker-Planck equation of a generalized type.
The formulation is then applied to the Haken-Zwanzing model for non-equilibrium phase transitions, and a prototype procedure for obtaining a stochastic Ginzburg-Landau type equation for the order parameter is clarified. Thus it turns out that the mode couplings of the order parameter to irrelevant macrovariables generate fluctuations of the order parameter in the ordered phase, but the variance due to these fluctuations does not diverge even near the instability point. In the critical region, the fluctuations have the critical dimensionality dc=2.


URL : http://ptp.ipap.jp/link?PTP/63/1865/
DOI : 10.1143/PTP.63.1865

[ Full Text PDF : FREE ACCESS (1436K) ] Citation:

References:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 57 (1988) pp. 1163-1166 :
    Chaotic Behaviour of Soliton-Like Pulses in a Driven Modified Kuramoto-Sivashinsky Equation
    Hidetoshi Konno and Hideo Soneda
  2. 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
  3. Progress of Theoretical Physics Vol. 65 No. 2 (1981) pp. 746-750 :
    Renormalization Group Approach to the Hard Mode Instability
    Jun-Ichiro Tada and Satoshi Takada
  4. Progress of Theoretical Physics Vol. 65 No. 6 (1981) pp. 1820-1834 :
    Anomalous Fluctuations near Nonequilibrium Soft Transitions. I
    Kazuko T. Mashiyama, Kiyohumi Takayoshi and Hazime Mori
  5. Progress of Theoretical Physics Vol. 66 No. 1 (1981) pp. 154-171 :
    Anomalous Fluctuations near Nonequilibrium Soft Transitions. II
    Kazuko T. Mashiyama and Hazime Mori
  6. Progress of Theoretical Physics Vol. 67 No. 1 (1982) pp. 98-117 :
    On the Contraction of Fast Driving Variables from Stochastic Processes
    Hiroshi Hasegawa, Masahiko Mizuno and Mahito Mabuchi
  7. Progress of Theoretical Physics Vol. 72 No. 6 (1984) pp. 1255-1257 :
    On the Influence of Weak Additive Noise on the Long Time Behaviour of the Correlation Functions for Multiplicative Stochastic Processes
    H. R. Brand

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