Equilibrium states for classical systems

C. Gruber, J. L. Lebowitz

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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{variant}, and for the spin correlation functions σ, are essentially equivalent for all ρ{variant}, 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.

Original languageEnglish (US)
Pages (from-to)11-18
Number of pages8
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - Feb 1975
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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