Fluctuation and relaxation of macrovariables
- 530 Downloads
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.
Key wordsRelaxation and fluctuation Markovian process propagation of extensive property birth and death process kinetic Weiss-lsing model Brownian motion generalized Fokker-Planck equation fluctuations far from equilibrium relaxation spectrum in critical states path integral
Unable to display preview. Download preview PDF.
- 1.N. G. van Kampen,Can. J. Phys. 39:551 (1961).Google Scholar
- 2.N. G. van Kampen, inFundamental Problems in Statistical Mechanics, (Proc. NUFFIC Int. Summer Courses in Science. The Netherland, August 1961), E. G. D. Cohen, ed., Amsterdam (1962), p. 173.Google Scholar
- 3.N. G. van Kampen, inFluctuation Phenomena in Solids, R. E. Burgess, Academic Press, New York-London.Google Scholar
- 4.R. Kubo, inSynergetics (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.Google Scholar
- 5.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
- 6.J. L. Doob,Ann. Math. 43:351 (1942); Ming Chen Wang and G. E. Uhlenbeck,Rev. Mod. Phys. 17:323 (1945).Google Scholar
- 7.R. Kubo,Rep. Progr. Phys. 29 (Part I):255 (1966).Google Scholar
- 8.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
- 9.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, inProgress in Optics, E. Wolf, ed., North-Holland, Amsterdam (1970), p. 241.Google Scholar
- 10.Th. W. Ruijgrok and T. A. Tjon, preprint.Google Scholar
- 11.H. A. Bethe,Phys. Rev. 54:955 (1938).Google Scholar