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Equilibrium states for classical systems

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Abstract

It is shown that the Dobrushin-Lanford-Ruelle equations for the probability measure μ, and the Kirkwood-Salsburg type equations for the lattice or continuum correlation functions ϱ, and for the spin correlation functions σ, are essentially equivalent for all ϱ, σ, and μ satisfying certain boundedness conditions. It is also noted that the lattice equations are identical to the equations for the stationary states of a certain Markoff process. This extends previous results of Ruelle, Brascamp and Holley who proved some of these equivalences for states.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique, Ecole Polytechnique Fédérale, Lausanne, Switzerland

    C. Gruber

  2. Belfer Graduate School of Science, Yeshiva University, New York, N.Y., USA

    J. L. Lebowitz

Authors
  1. C. Gruber
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  2. J. L. Lebowitz
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Additional information

Communicated by G. Gallavotti

Research supported in part by AFOSR Grant No. 73-2430A.

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Gruber, C., Lebowitz, J.L. Equilibrium states for classical systems. Commun.Math. Phys. 41, 11–18 (1975). https://doi.org/10.1007/BF01608543

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  • DOI: https://doi.org/10.1007/BF01608543

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