Journal of Statistical Physics

, Volume 153, Issue 3, pp 412–441 | Cite as

Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems

  • Tatsuro Yuge
  • Takahiro Sagawa
  • Ayumu Sugita
  • Hisao Hayakawa


For open systems described by the quantum Markovian master equation, we study a possible extension of the Clausius equality to quasistatic operations between nonequilibrium steady states (NESSs). We investigate the excess heat divided by temperature (i.e., excess entropy production) which is transferred into the system during the operations. We derive a geometrical expression for the excess entropy production, which is analogous to the Berry phase in unitary evolution. Our result implies that in general one cannot define a scalar potential whose difference coincides with the excess entropy production in a thermodynamic process, and that a vector potential plays a crucial role in the thermodynamics for NESSs. In the weakly nonequilibrium regime, we show that the geometrical expression reduces to the extended Clausius equality derived by Saito and Tasaki (J. Stat. Phys. 145:1275, 2011). As an example, we investigate a spinless electron system in quantum dots. We find that one can define a scalar potential when the parameters of only one of the reservoirs are modified in a non-interacting system, but this is no longer the case for an interacting system.


Nonequilibrium steady state Entropy production Clausius equality Geometrical phase Quantum Markovian master equation 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Tatsuro Yuge
    • 1
  • Takahiro Sagawa
    • 2
    • 3
    • 4
  • Ayumu Sugita
    • 5
  • Hisao Hayakawa
    • 3
  1. 1.Department of PhysicsOsaka UniversityToyonakaJapan
  2. 2.The Hakubi CenterKyoto UniversityKyotoJapan
  3. 3.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan
  4. 4.Department of Basic ScienceThe University of TokyoTokyoJapan
  5. 5.Department of Applied PhysicsOsaka City UniversityOsakaJapan

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