Journal of Statistical Physics

, Volume 148, Issue 3, pp 480–501 | Cite as

Quantum Fluctuation Relations for the Lindblad Master Equation

Article

Abstract

An open quantum system interacting with its environment can be modeled under suitable assumptions as a Markov process, described by a Lindblad master equation. In this work, we derive a general set of fluctuation relations for systems governed by a Lindblad equation. These identities provide quantum versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula.

Keywords

Fluctuation relations Quantum Markovian process Fluctuation Dissipation Theorem 

Notes

Acknowledgements

R.C. thanks K. Gawȩdzki for pointing out the fact that the Lindbladian character of Eq. (43) is non-trivial and the relation with detailed balance. R.C. acknowledges the support of the Koshland center for basic research. K.M. thanks M. Bauer and H. Orland for useful comments and S. Mallick for useful remarks on the manuscript. Results similar to those presented here were also reached independently by K. Gawȩdzki and S. Attal some time ago [7].

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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Laboratoire J. A. Dieudonné, UMR CNRS 6621Université de Nice Sophia-AntipolisNice Cedex 02France
  2. 2.Institut de Physique ThéoriqueCEA SaclayGif-sur-YvetteFrance

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