Journal of Statistical Physics

, Volume 156, Issue 1, pp 55–65 | Cite as

Equivalent Definitions of the Quantum Nonadiabatic Entropy Production

  • Jordan M. Horowitz
  • Takahiro Sagawa


The nonadiabatic entropy production is a useful tool for the thermodynamic analysis of continuously dissipating, nonequilibrium steady states. For open quantum systems, two seemingly distinct definitions for the nonadiabatic entropy production have appeared in the literature, one based on the quantum relative entropy and the other based on quantum trajectories. We show that these two formulations are equivalent. Furthermore, this equivalence leads us to a proof of the monotonicity of the quantum relative entropy under a special class of completely-positive, trace-preserving quantum maps, which circumvents difficulties associated with the noncommuntative structure of operators.


Quantum nonequilibrium thermodynamics Nonadiabatic entropy production Quantum relative entropy monotonicity 



We are grateful to Franco Fagnola for providing the proof of the existence of a privileged representation for CPTP maps. JMH is supported by ARO MURI grant W911NF-11-1-0268 and TS by JSPS KAKENHI Grant Nos. 25800217 and 22340114.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of Massachusetts at BostonBostonUSA
  2. 2.Department of Basic ScienceThe University of TokyoTokyoJapan

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