Abstract
We prove that any stationary state describing an infinite classical system which is “stable” under local perturbations (and possesses some strong time clustering properties) must satisfy the “classical” KMS condition. (This in turn implies, quite generally, that it is a Gibbs state.) Similar results have been proven previously for quantum systems by Haag et al. and for finite classical systems by Lebowitz et al.
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Communicated by K. Hepp
Supported by N.S.F. Grant MPS 71-03375 A03. Part of this work carried out at the Courant Institute where it was supported by N.S.F. Grant GP-37069X.
Supported in part by AFOSR Grant #73-2430 and N.S.F. Grant MP S75-20638.
Supported by N.S.F. Grant # GP33136X-2. Part of this work was carried out at the Institute for Advanced Study.
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Aizenman, M., Gallavotti, G., Goldstein, S. et al. Stability and equilibrium states of infinite classical systems. Commun.Math. Phys. 48, 1–14 (1976). https://doi.org/10.1007/BF01609407
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DOI: https://doi.org/10.1007/BF01609407