Stability and equilibrium states of infinite classical systems |
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| Authors: | Michael Aizenman Giovanni Gallavotti Sheldon Goldstein Joel L Lebowitz |
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| Institution: | (1) Department of Physics and Mathematics, Princeton University, Princeton, N.J., USA;(2) Istituto Matematico, University di Roma, I-00185 Roma, Italy;(3) Department of Mathematics, Cornell University, Ithaca, N.Y., USA;(4) Belfer Graduate School of Science, Yeshiva University, 10033 New York, N.Y., USA |
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| 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.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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