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Statistical mechanics of a one-dimensional lattice gas

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.

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Bibliography

  1. 1.

    Arnold, V. I., etA. Avez: Problèmes ergodiques de la mécanique classique. Paris: Gauthier-Villars 1967.

  2. 2.

    Fisher, M. E.: The theory of condensation (Sec. 6.). Lecture given at the Centennial Conference on Phase Transformation at the University of Kentucky, 1965.

  3. 3.

    Jacobs, K.: Lecture notes on ergodic theory. Aarhus Universitet (1962–1963).

  4. 4.

    Robinson, D., andD. Ruelle: Mean entropy of states in classical statistical mechanics. Commun. Math. Phys.5, 288–300 (1967).

  5. 5.

    van Hove, L.: L'intégrale de configuration pour les systèmes de particules à une dimension. Physica16, 137–143 (1950).

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Ruelle, D. Statistical mechanics of a one-dimensional lattice gas. Commun.Math. Phys. 9, 267–278 (1968). https://doi.org/10.1007/BF01654281

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Keywords

  • Neural Network
  • Phase Transition
  • Dynamical System
  • Statistical Physic
  • Equilibrium State