Journal of Statistical Physics

, Volume 9, Issue 1, pp 51–96 | Cite as

Fluctuation and relaxation of macrovariables

  • Ryogo Kubo
  • Kazuhiro Matsuo
  • Kazuo Kitahara


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 words

Relaxation 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 


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Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • Ryogo Kubo
    • 1
  • Kazuhiro Matsuo
    • 1
  • Kazuo Kitahara
    • 2
  1. 1.Department of PhysicsUniversity of TokyoTokyoJapan
  2. 2.Chimie Physique II, Faculté des SciencesUniversité Libre de BruxellesBrusselsBelgium

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