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 TMF, 1974, Volume 21, Number 3, Pages 354–366 (Mi tmf3904)

Quasiinvariants of the motion and existence of the $\varepsilon$-limit in the nonequilibrium statistical operator method

M. I. Auslender

Abstract: 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.

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English version:
Theoretical and Mathematical Physics, 1974, 21:3, 1198–1207

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Citation: M. I. Auslender, “Quasiinvariants of the motion and existence of the $\varepsilon$-limit in the nonequilibrium statistical operator method”, TMF, 21:3 (1974), 354–366; Theoret. and Math. Phys., 21:3 (1974), 1198–1207

Citation in format AMSBIB
\Bibitem{Aus74} \by M.~I.~Auslender \paper Quasiinvariants of the motion and existence of the $\varepsilon$-limit in the nonequilibrium statistical operator method \jour TMF \yr 1974 \vol 21 \issue 3 \pages 354--366 \mathnet{http://mi.mathnet.ru/tmf3904} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=479231} \zmath{https://zbmath.org/?q=an:0313.60071} \transl \jour Theoret. and Math. Phys. \yr 1974 \vol 21 \issue 3 \pages 1198--1207 \crossref{https://doi.org/10.1007/BF01038098} 

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This publication is cited in the following articles:
1. V. P. Vstovskii, “Macroscopic description of open dynamical systems”, Theoret. and Math. Phys., 31:3 (1977), 540–548
2. M. I. Auslender, V. P. Kalashnikov, “Equivalence of two forms of the nonequilibrium statistical operator”, Theoret. and Math. Phys., 58:2 (1984), 196–202
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