Geodesic
Electrical conductivity of charged particle systems and Zubarev's nonequilibrium statistical operator method
Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 1, pp. 90-126

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One of the fundamental problems in physics that are not yet rigorously solved is the statistical mechanics of nonequilibrium processes. An important contribution to describing irreversible behavior starting from reversible Hamiltonian dynamics was given by D. N. Zubarev, who invented the method of the nonequilibrium statistical operator. We discuss this approach, in particular, the extended von Neumann equation, and as an example consider the electrical conductivity of a system of charged particles. We consider the selection of the set of relevant observables. We show the relation between kinetic theory and linear response theory. Using thermodynamic Green's functions, we present a systematic treatment of correlation functions, but the convergence needs investigation. We compare different expressions for the conductivity and list open questions.
Keywords: nonequilibrium statistical operator, electrical conductivity, linear response theory, kinetic theory, Kubo–Greenwood approach. 
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     author = {G. R\"opke},
     title = {Electrical conductivity of charged particle systems and {Zubarev's} nonequilibrium statistical operator method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {90--126},
     publisher = {mathdoc},
     volume = {194},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_194_1_a4/}
}
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G. Röpke. Electrical conductivity of charged particle systems and Zubarev's nonequilibrium statistical operator method. Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 1, pp. 90-126. http://geodesic.mathdoc.fr/item/TMF_2018_194_1_a4/