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The Kirkwood-Salsburg equations: Solutions and spectral properties

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Abstract

It is shown that the Kirkwood-Salsburg equations for a classical lattice gas are equivalent to the Dobrushin-Lanford-Ruelle equilibrium equations. The term “Kirkwood-Salsburg equations” is used here in a restricted sense, and thus the known result for a larger system of equations is improved (see Table 1). Some information on the spectrum of the Kirkwood-Salsburg operator is found in connection with zeros of partition functions. An example is given to show that the Kirkwood-Salsburg equations can have other solutions than states in the space of uniformly bounded correlation functions.

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Authors and Affiliations

  1. The Institute for Advanced Study, Princeton, New Jersey, USA

    Herm Jan Brascamp

  2. Department of Physics, Princeton University, 08540, Princeton, N.J., USA

    Herm Jan Brascamp

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  1. Herm Jan Brascamp
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Communicated by G. Gallavotti

Supported by National Science Foundation Grant GP-40768X.

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Brascamp, H.J. The Kirkwood-Salsburg equations: Solutions and spectral properties. Commun.Math. Phys. 40, 235–247 (1975). https://doi.org/10.1007/BF01610000

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  • DOI: https://doi.org/10.1007/BF01610000

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