Journal of Statistical Physics

, Volume 108, Issue 5, pp 787–829

Mathematical Theory of Non-Equilibrium Quantum Statistical Mechanics

  • V. Jakšić
  • C.-A. Pillet

DOI: 10.1023/A:1019818909696

Cite this article as:
Jakšić, V. & Pillet, CA. Journal of Statistical Physics (2002) 108: 787. doi:10.1023/A:1019818909696


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 mechanicsLiouvilleanopen systemsentropy productionsteady stateC*-algebra

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • V. Jakšić
    • 1
  • C.-A. Pillet
    • 2
    • 3
  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada
  2. 2.PHYMATUniversité de ToulonLa Garde CedexFrance
  3. 3.FRUMAMCPT-CNRS LuminyMarseille Cedex 9France