Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     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},
     year = {1974},
     volume = {21},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1974_21_3_a6/}
}
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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/

[1] D. N. Zubarev, Neravnovesnaya statisticheskaya termodinamika, «Nauka», 1971

[2] V. P. Kalashnikov, TMF, 9 (1971), 94

[3] D. N. Zubarev, V. P. Kalashnikov, TMF, 3 (1970), 126 | MR

[4] K. Moren, Metody gilbertova prostranstva, «Mir», 1965 | MR

[5] N. Burbaki, Funktsii deistvitelnogo peremennogo. Elementarnaya teoriya, «Nauka», 1965 | MR

[6] D. Ryuel, Statisticheskaya mekhanika. Strogie rezultaty, «Mir», 1971

[7] R. Haag, N. M. Hugengoltz, M. Winnik, Commun. Math. Phys., 5 (1967), 215 | DOI | MR | Zbl

[8] J. Ginibre, J. Math. Phys., 6 (1965), 238 | DOI | MR | Zbl

[9] V. P. Kalashnikov, Dokt. diss., Institut fiziki metallov AN SSSR, Sverdlovsk, 1972