Fluctuation and relaxation of macrovariables (original) (raw)
Abstract
Assuming that a macrovariable follows a Markovian process, the extensive property of its probability distribution is proved to propagate. This is a generalization of the Gaussian properties of the equilibrium distribution to nonequilibrium nonstationary processes. It is basically a WKB-like asymptotic evaluation in the inverse of the size of the macrosystem. Evolution of the variable along the most probable path and fluctuation properties around the path are considered from a general point of view with an emphasis on the relation of nonlinearity of evolution and the associated fluctuation. Anomalous behavior of the fluctuation is discussed in connection with unstable, critical, or marginal states. A general treatment is given for the asymptotic properties of relaxation eigenmodes.
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References
- N. G. van Kampen,Can. J. Phys. 39:551 (1961).
Google Scholar - N. G. van Kampen, in_Fundamental Problems in Statistical Mechanics_, (Proc. NUFFIC Int. Summer Courses in Science. The Netherland, August 1961), E. G. D. Cohen, ed., Amsterdam (1962), p. 173.
- N. G. van Kampen, in_Fluctuation Phenomena in Solids_, R. E. Burgess, Academic Press, New York-London.
- R. Kubo, in_Synergetics_ (Proc. Symp. Synergetics, 1972, Schloss Elmau), H. Haken and B. G. Teubner, eds., Stuttgart (1973); Contributed paper, IUPAP Conf. on Statistical Mechanics, Univ. Chicago, 1971.
- R. B. Griffiths, C. Y. Weng, and J. S. Langer,Phys. Rev. 149:301 (1966); M. Suzuki and R. Kubo,J. Phys. Soc. Japan 24:51 (1968); W. Weidlich,Collective Phenomena 1:51 (1972).
Google Scholar - J. L. Doob,Ann. Math. 43:351 (1942); Ming Chen Wang and G. E. Uhlenbeck,Rev. Mod. Phys. 17:323 (1945).
Google Scholar - R. Kubo,Rep. Progr. Phys. 29 (Part I):255 (1966).
Google Scholar - D. K. C. MacDonald,Phil. Mag. 45:63 (1954),Phys. Rev. 108:541 (1957); D. M. Middleton,J. Appl. Phys. 22:1143,1153 (1951); N. G. van Kampen,Phys. Rev. 110:319 (1958);Physica 26:585 (1960).
Google Scholar - F. T. Arecchi, V. Degiorgio, and B. Querzola,Phys. Rev. Letters 19:1168 (1967); F. T. Arecchi and V. Degiorgio,Phys. Rev. A 3:1108 (1971); H. Risken, in_Progress in Optics_, E. Wolf, ed., North-Holland, Amsterdam (1970), p. 241.
Google Scholar - Th. W. Ruijgrok and T. A. Tjon, preprint.
- H. A. Bethe,Phys. Rev. 54:955 (1938).
Google Scholar
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Authors and Affiliations
- Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo, Japan
Ryogo Kubo & Kazuhiro Matsuo - Chimie Physique II, Faculté des Sciences, Université Libre de Bruxelles, Brussels, Belgium
Kazuo Kitahara
Authors
- Ryogo Kubo
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Kubo, R., Matsuo, K. & Kitahara, K. Fluctuation and relaxation of macrovariables.J Stat Phys 9, 51–96 (1973). https://doi.org/10.1007/BF01016797
- Received: 13 April 1973
- Issue Date: September 1973
- DOI: https://doi.org/10.1007/BF01016797