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Communications in Mathematical Physics

, Volume 54, Issue 1, pp 81–96 | Cite as

Stationary solutions of the bogoliubov hierarchy equations in classical statistical mechanics. 2

  • B. M. Gurevich
  • Iu. M. Suhov
Article

Abstract

In the preceding paper under the same title we have formulated a theorem which describes the set of states (i.e., probability measures on phase space of an infinite system of particles inRv) corresponding to stationary solutions of the BBGKY hierarchy. We have proved the following statement: ifG is a Gibbs measure (Gibbs random point field) corresponding to a stationary solution of the BBGKY hierarchy, then its generating function satisfies a differential equation which is “conjugated” to the BBGKY hierarchy. The present paper deals with the investigation of the “conjugated” equation for the generating function in particular cases.

Keywords

Neural Network Generate Function Phase Space Complex System Probability Measure 
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References

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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • B. M. Gurevich
    • 1
  • Iu. M. Suhov
    • 2
    • 3
  1. 1.Laboratory of Statistical MethodsMoscow State UniversityMoscowUSSR
  2. 2.Centre de Physique ThéoriqueCNRSMarseilleFrance
  3. 3.UER Marseille-LuminyUniversité d'Aix-Marseille IIF-MarseilleFrance

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