Communications in Mathematical Physics

, Volume 5, Issue 5, pp 324–329 | Cite as

A variational formulation of equilibrium statistical mechanics and the Gibbs phase rule

  • D. Ruelle


It is shown that for an infinite lattice system, thermodynamic equilibrium is the solution of a variational problem involving a mean entropy of states introduced earlier [2]. As an application, a version of the Gibbs phase rule is proved.


Entropy Neural Network Statistical Physic Complex System Nonlinear Dynamics 
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  1. 1.
    Gallavotti, G., andS. Miracle-Sole: Statistical mechanics of lattice systems. Commun. Math. Phys.5, 317 (1967).Google Scholar
  2. 2.
    Robinson, D. W., andD. Ruelle: Mean entropy of states in classical statistical mechanics. Commun. Math. Phys.5, 288 (1967).Google Scholar
  3. 3.
    Ruelle, D.: J. Math. Phys.6, 201–220 (1965).Google Scholar
  4. 4.
    -- The states of classical statistical mechanics. Preprint.Google Scholar

Copyright information

© Springer-Verlag 1967

Authors and Affiliations

  • D. Ruelle
    • 1
  1. 1.Institut des Hautes Etudes Scientifiques91. Bures-sur-YvetteFrance

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