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Prog. Theor. Phys. Vol. 56 No. 2 (1976) pp. 477-493

[ Full Text PDF : FREE ACCESS (1119K) ]

Scaling Theory of Non-Equilibrium Systems near the Instability Point. II

— Anomalous Fluctuation Theorems in the Extensive Region —

Masuo Suzuki

Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo

(Received January 30, 1976)

Abstract:

The scaling idea for transient phenomena is applied to investigating anomalous fluctuations in the extensive region. The scaling law for the most probable path is derived. It is proved generally that fluctuations around it are enhanced anomalously proportionally to the inverse square of a deviation δ of the initial system from the instability point (anomalous fluctuation theorem). This is also expressed as the fluctuation-intensity relation (i.e., σI ∝{\dotI(t) / \dotI(0) }2) in the scaling regime. Fluctuations of higher order are also discussed. The enhancement factor of the n-th cumulant is proportional to δ-n. The profile of the anomalous fluctuation is given essentially by the square of the first moment with the most probable path in its argument for the Kramers-Moyal equation. Some applications of the general theory are given to Kubo's model, the laser model, an asymmetric laser model and superradiance. It is predicted that the fluctuation of intensity of superradiance shows double anomalous enhancements before and after the maximum time tm of the intensity.


URL : http://ptp.ipap.jp/link?PTP/56/477/
DOI : 10.1143/PTP.56.477

[ Full Text PDF : FREE ACCESS (1119K) ] Citation:

References:

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    See also references cited in Ref. 7).
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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 57 No. 2 (1977) pp. 380-392 :
    Scaling Theory of Non-Equilibrium Systems near the Instability Point. III
    Masuo Suzuki
  2. Progress of Theoretical Physics Vol. 57 No. 2 (1977) pp. 410-425 :
    Dynamics of Fluctuations in Unstable Systems. I
    Kyozi Kawasaki
  3. Progress of Theoretical Physics Vol. 57 No. 3 (1977) pp. 746-758 :
    On the Thermodynamic Limit in Equilibrium and Non-Equilibrium Systems
    Masuo Suzuki
  4. Progress of Theoretical Physics Vol. 57 No. 6 (1977) pp. 1874-1885 :
    Nonlinear Fluctuations Associated with Instabilities in Dissipative Systems
    Ki-ichi Nakamura
  5. Progress of Theoretical Physics Vol. 58 No. 1 (1977) pp. 175-189 :
    Dynamics of Fluctuations in Unstable Systems. II
    Kyozi Kawasaki
  6. Progress of Theoretical Physics Vol. 60 No. 3 (1978) pp. 683-698 :
    Nonlinear Dynamics of First Order Phase Transition
    Chikara Murakami and Hiroyuki Tomita
  7. Progress of Theoretical Physics Vol. 61 No. 4 (1979) pp. 1023-1033 :
    Pseudo-Critical Dynamics in First-Order Transitions
    Hiroshi Ikeda
  8. Progress of Theoretical Physics Vol. 64 No. 4 (1980) pp. 1127-1137 :
    A Method for Solving a Stochastic Differential Equation
    Yoshiyasu Hamada
  9. Progress of Theoretical Physics Vol. 65 No. 3 (1981) pp. 828-849 :
    Phase Transition and Slowing Down in Non-Equilibrium Stochastic Processes
    Masuo Suzuki, Kunihiko Kaneko and Fumiyoshi Sasagawa
  10. Progress of Theoretical Physics Vol. 66 No. 4 (1981) pp. 1230-1249 :
    Nonlinear Theory of Sound Waves near Critical Points. I
    Akira Onuki
  11. Progress of Theoretical Physics Vol. 67 No. 3 (1982) pp. 804-815 :
    Asymptotic Property of Probability Distribution in the Relaxation from an Unstable Point
    Takashi Kunisawa and Jinya Otsuka
  12. Progress of Theoretical Physics Vol. 68 No. 1 (1982) pp. 98-115 :
    Critical Slowing Down in Stochastic Precesses. II
    Masuo Suzuki, Shinji Takesue and Fumiyoshi Sasagawa
  13. Progress of Theoretical Physics Vol. 71 No. 2 (1984) pp. 267-281 :
    Scaling Property of the Relative Diffusion of Charged Particles in Turbulent Electric Fields. I
    Masuo Suzuki
  14. Progress of Theoretical Physics Vol. 74 No. 5 (1985) pp. 997-1004 :
    Relative Motion in Stochastic Velocity and Force Fields
    Yutaka Inaba and Masuo Suzuki
  15. Progress of Theoretical Physics Supplement No.64 (1978) pp. 402-424 :
    Scaling Theory of Transient Nonlinear Fluctuations and Formation of Macroscopic Order
    Masuo Suzuki
  16. Progress of Theoretical Physics Supplement No.69 (1980) pp. 160-173 :
    Fluctuation and Relaxation in Stochastic Systems
    Masuo Suzuki
  17. Progress of Theoretical Physics Supplement No.79 (1984) pp. 125-140 :
    Fluctuation and Formation of Macroscopic Order in Non-Equilibrium Systems
    Masuo Suzuki
  18. Progress of Theoretical Physics Supplement No.195 (2012) pp. 114-119 :
    Macroscopic Order Formation,Inflation Mechanism and Entropy Change
    Masuo Suzuki

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