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Topics in non-equilibrium quantum statistical mechanics. (English) Zbl 1126.82032
Attal, Stéphane (ed.) et al., Open quantum systems III. Recent developments. Lecture notes of the summer school, Grenoble, France, June 16th – July 4th 2003. Berlin: Springer (ISBN 3-540-30993-4/pbk). Lecture Notes in Mathematics 1882, 1-66 (2006).
The framework is the mathematical formalism of algebraic quantum statistical mechanics and its relation with nonequilibrium steady states (NESS, in statistical mechanics), of which the general properties are discussed, together with entropy production. Given this prerequisite, open quantum systems are analyzed in a detailed way, mainly with respect to the first and the second law of thermodynamics and also with respect to its linear response theory. A special case of open system is provided by the free Fermi gas reservoir. The second part of the paper is devoted to the study of the nonequilibrium statistical simple electronic black-box model introduced elsewhere by the authors (paper in preparation). Following a careful description of this model, one considers its thermodynamics (heat and charge fluxes, entropy production, Onsager’s relations, Kubo’s formulae, Fermi golden rule (FRG) thermodynamics). Both the Schrödinger’s picture and the Heisenberg’s pictures are involved.
For the entire collection see [Zbl 1103.81002].

82C35 Irreversible thermodynamics, including Onsager-Machlup theory
82C03 Foundations of time-dependent statistical mechanics
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