Mathematical Theory of Non-Equilibrium Quantum Statistical Mechanics

Claude-Alain Pillet (1, 2, 3, 4) , Vojkan Jaksic (5)

1 CPT - E5 Physique statistique et systèmes complexes
2 FRUMAM - Fédération de Recherche des Unités de MAthématiques de Marseille
3 CPT - Centre de Physique Théorique - UMR 6207
4 CPT - Centre de Physique Théorique - UMR 7332
5 Department of Mathematics and Statistics [Montréal]

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.

Mots clés: Nonequilibrium quantum statistical mechanics; Liouvillean; open systems; entropy production; steady state; C*-algebra

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique Générale [physics.gen-ph]; Algèbres d'opérateurs [math.OA]; Systèmes dynamiques [math.DS]; Théorie spectrale [math.SP]

Claude-Alain Pillet, Vojkan Jaksic. Mathematical Theory of Non-Equilibrium Quantum Statistical Mechanics. Journal of Statistical Physics, 2002, 108, pp.787 - 829. ⟨10.1023/A:1019818909696⟩. ⟨hal-00005459⟩