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Mathematical Theory of Non-Equilibrium Quantum Statistical Mechanics

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Abstract

We review and further develop a mathematical framework for non-equilibrium quantum statistical mechanics recently proposed in refs. 1–7. In the algebraic formalism of quantum statistical mechanics we introduce notions of non-equilibrium 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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC, Canada, H3A 2K6

    V. Jakšić

  2. PHYMAT, Université de Toulon, B.P. 132, F-83957, La Garde Cedex, France

    C.-A. Pillet

  3. FRUMAM, CPT-CNRS Luminy, Case 907, F-13288, Marseille Cedex 9, France

    C.-A. Pillet

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  1. V. Jakšić
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Jakšić, V., Pillet, CA. Mathematical Theory of Non-Equilibrium Quantum Statistical Mechanics. Journal of Statistical Physics 108, 787–829 (2002). https://doi.org/10.1023/A:1019818909696

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