Quasiinvariants of the motion and existence of the $\varepsilon$-limit in the nonequilibrium statistical operator method
Teoretičeskaâ i matematičeskaâ fizika, Tome 21 (1974) no. 3, pp. 354-366
Voir la notice de l'article provenant de la source Math-Net.Ru
In the framework of the axiomatic approach to the thermodynamic limit developed by
Ruelle [6] and Haag et al. [7], an investigation is made of the existence of a nonequilibrium stationary state generated by a retarded solution of the Liouville equation, i.e., of the limit as
$\varepsilon\to+0$ of states generated by quasiinvariants of the motion obtained by causal smoothing of the coarse-grained statistical operator [2, 3]. It is shown that the $\varepsilon$-limit exists if the coarse-grained state and the operators of time evolution of the variables at positive times in the thermodynamic limit satisfy a definite condition, which is intimately related to the condition of correlation weakening. The proof is based on the use of the
$n$-quasiinvariants of the motion [3] and the Yosida–Kakutani ergodic theorem.
@article{TMF_1974_21_3_a6,
author = {M. I. Auslender},
title = {Quasiinvariants of the motion and existence of the $\varepsilon$-limit in the nonequilibrium statistical operator method},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {354--366},
publisher = {mathdoc},
volume = {21},
number = {3},
year = {1974},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1974_21_3_a6/}
}
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%0 Journal Article %A M. I. Auslender %T Quasiinvariants of the motion and existence of the $\varepsilon$-limit in the nonequilibrium statistical operator method %J Teoretičeskaâ i matematičeskaâ fizika %D 1974 %P 354-366 %V 21 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1974_21_3_a6/ %G ru %F TMF_1974_21_3_a6
M. I. Auslender. Quasiinvariants of the motion and existence of the $\varepsilon$-limit in the nonequilibrium statistical operator method. Teoretičeskaâ i matematičeskaâ fizika, Tome 21 (1974) no. 3, pp. 354-366. http://geodesic.mathdoc.fr/item/TMF_1974_21_3_a6/