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Communications in Mathematical Physics

, Volume 48, Issue 1, pp 1–14 | Cite as

Stability and equilibrium states of infinite classical systems

  • Michael Aizenman
  • Giovanni Gallavotti
  • Sheldon Goldstein
  • Joel L. Lebowitz
Article

Abstract

We prove that any stationary state describing an infinite classical system which is “stable” under local perturbations (and possesses some strong time clustering properties) must satisfy the “classical” KMS condition. (This in turn implies, quite generally, that it is a Gibbs state.) Similar results have been proven previously for quantum systems by Haag et al. and for finite classical systems by Lebowitz et al.

Keywords

Neural Network Statistical Physic Equilibrium State Complex System Stationary State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Michael Aizenman
    • 1
  • Giovanni Gallavotti
    • 2
  • Sheldon Goldstein
    • 3
  • Joel L. Lebowitz
    • 4
  1. 1.Department of Physics and MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Istituto MatematicoUniversity di RomaRomaItaly
  3. 3.Department of MathematicsCornell UniversityIthacaUSA
  4. 4.Belfer Graduate School of ScienceYeshiva UniversityNew YorkUSA

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