Extended Clausius Relation and Entropy for Nonequilibrium Steady States in Heat Conducting Quantum Systems

Keiji Saito, Hal Tasaki

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Recently, in their attempt to construct steady state thermodynamics (SST), Komatsu, Nakagawa, Sasa, and Tasaki found an extension of the Clausius relation to nonequilibrium steady states in classical stochastic processes. Here we derive a quantum mechanical version of the extended Clausius relation. We consider a small system of interest attached to large systems which play the role of heat baths. By only using the genuine quantum dynamics, we realize a heat conducting nonequilibrium steady state in the small system. We study the response of the steady state when the parameters of the system are changed abruptly, and show that the extended Clausius relation, in which "heat" is replaced by the "excess heat", is valid when the temperature difference is small. Moreover we show that the entropy that appears in the relation is similar to von Neumann entropy but has an extra symmetrization with respect to time-reversal. We believe that the present work opens a new possibility in the study of nonequilibrium phenomena in quantum systems, and also confirms the robustness of the approach by Komatsu et al.

Original languageEnglish
Pages (from-to)1275-1290
Number of pages16
JournalJournal of Statistical Physics
Issue number5
Publication statusPublished - 2011 Dec
Externally publishedYes


  • Clausius relation
  • Excess heat
  • Nonequilibrium steady state
  • Quantum heat conduction

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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