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Communications in Mathematical Physics

, Volume 30, Issue 1, pp 35–44 | Cite as

Correlation functions and the uniqueness of the state in classical statistical mechanics

  • A. Lenard
Article

Abstract

A general criterion is derived which assures the uniqueness of the state of a classical statistical mechanical system in terms of a given system of correlation functions. The criterion is\(\sum\limits_k {(m_{k + j}^A )} ^{ - 1/k} = \infty\) for allj and all bounded setsA, where
$$m_k^A = (k!)^{ - 1} \int\limits_A \cdots \int\limits_A {\varrho _k } (x_1 , \ldots ,x_k )dx_1 \ldots dx_1 .$$

Keywords

Neural Network Statistical Physic Assure Correlation Function Complex System 
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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References

  1. 1.
    Akhiezer, N.I.: The classical moment problem and some related questions in analysis. Edinburgh: Oliver and Boyd 1965.Google Scholar
  2. 2.
    Carleman, T.: Les fonctions quasi analytiques, Chapter III. Paris: Gauthier-Villars 1926.Google Scholar
  3. 3.
    Halmos, P.R.: Measure theory. New York: Van Nostrand 1950.Google Scholar
  4. 4.
    Ruelle, D.: Statistical mechanics, rigorous results. New York: Benjamin 1969.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • A. Lenard
    • 1
  1. 1.Institute for Advanced StudyPrincetonUSA

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