Letters in Mathematical Physics

, Volume 75, Issue 1, pp 17–23 | Cite as

A Remark on the Strict Positivity of the Entropy Production

Article

Abstract

We establish an algebraic criterion which ensures the strict positivity of the entropy production in quantum models consisting of a small system coupled to thermal reservoirs at different temperatures.

Keywords

Non-equilibrium steady state entropy production weak coupling theory 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aschbacher, W.H. Jakšić, V. Pautrat, Y. Pillet, C.-A.: Topics in non-equilibrium quantum statistical mechanics, Springer lecture notes in mathematics, (to appear), mp_arc 05-207Google Scholar
  2. 2.
    Aschbacher W.H. Pillet C.-A. (2003). Non-equilibrium steady states of the XY chain. J. Stat. Phys. 112: 1153MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Davies E.B. (1974). Markovian master equations. Comm. Math. Phys. 39: 91MATHCrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Eckmann J.-P., Pillet C.-A., Rey-Bellet L. (1999). Entropy production in non-linear, thermally driven Hamiltronian systems. J. Stat. Phys. 95: 305MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Jakšić V., Pillet C.-A. (2002). Mathematical theory of non-equilibrium quantum statistical mechanics. J. Stat. Phys. 108: 787CrossRefGoogle Scholar
  6. 6.
    Jakšić V., Pillet C.-A. (2002). Non-equilibrium steady states of finite quantum systems coupled to thermal reservoirs. Comm. Math. Phys. 226: 131CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    Ruelle D. (2001). Entropy production in quantum spin systems. Comm. Math. Phys. 224: 3MATHCrossRefADSMathSciNetGoogle Scholar
  8. 8.
    Spohn H. (1976). Approach to equilibrium for completely positive dynamical semigroups of n-level systems. Rep. Math. Phys. 10: 189CrossRefMathSciNetGoogle Scholar
  9. 9.
    Spohn H. (1977). An algebraic condition for the approach to equilibrium of an open n-level system. Lett. Math. Phys. 2: 33MATHCrossRefADSMathSciNetGoogle Scholar
  10. 10.
    Spohn H., Lebowitz J.L. (1978). Irreversible thermodynamics for quantum systems weakly coupled to thermal reservoirs. Adv. Chem. Phys. 38: 109CrossRefGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Zentrum Mathematik, M5Technische Universität MünchenGarchingGermany

Personalised recommendations