Mathematical theory of non-equilibrium quantum statistical mechanics. (English) Zbl 1025.82011

Summary: We review and further develop a mathematical framework for nonequilibrium quantum statistical mechanics recently proposed by the authors and D. Ruelle. In the algebraic formalism of quantum statistical mechanics we introduce notions of nonequilibrium steady states, entropy production and heat fluxes, and study their properties. Our basic paradigm is a model of a small (finite) quantum system coupled to several independent thermal reservoirs. We exhibit examples of such systems which have strictly positive entropy production.


82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
46L60 Applications of selfadjoint operator algebras to physics
82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics
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