Journal of Statistical Physics

, Volume 108, Issue 5, pp 787-829

First online:

Mathematical Theory of Non-Equilibrium Quantum Statistical Mechanics

  • V. JakšićAffiliated withDepartment of Mathematics and Statistics, McGill University
  • , C.-A. PilletAffiliated withPHYMAT, Université de ToulonFRUMAM, CPT-CNRS Luminy

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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.

Nonequilibrium quantum statistical mechanics Liouvillean open systems entropy production steady state C*-algebra