Journal of Statistical Physics

, Volume 108, Issue 5–6, 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 mechanics Liouvillean open systems entropy production steady state C*-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

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