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Communications in Mathematical Physics

, Volume 9, Issue 4, pp 267–278 | Cite as

Statistical mechanics of a one-dimensional lattice gas

  • D. Ruelle
Article

Abstract

We study the statistical mechanics of an infinite one-dimensional classical lattice gas. Extending a result ofvan Hove we show that, for a large class of interactions, such a system has no phase transition. The equilibrium state of the system is represented by a measure which is invariant under the effect of lattice translations. The dynamical system defined by this invariant measure is shown to be aK-system.

Keywords

Neural Network Phase Transition Dynamical System Statistical Physic Equilibrium 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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Bibliography

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    Arnold, V. I., etA. Avez: Problèmes ergodiques de la mécanique classique. Paris: Gauthier-Villars 1967.Google Scholar
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    Fisher, M. E.: The theory of condensation (Sec. 6.). Lecture given at the Centennial Conference on Phase Transformation at the University of Kentucky, 1965.Google Scholar
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    Jacobs, K.: Lecture notes on ergodic theory. Aarhus Universitet (1962–1963).Google Scholar
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    Robinson, D., andD. Ruelle: Mean entropy of states in classical statistical mechanics. Commun. Math. Phys.5, 288–300 (1967).Google Scholar
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    van Hove, L.: L'intégrale de configuration pour les systèmes de particules à une dimension. Physica16, 137–143 (1950).Google Scholar

Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • D. Ruelle
    • 1
  1. 1.I.H.E.S.91. Bures-sur-Yvette

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