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

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Abstract

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.

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Authors and Affiliations

  1. Graduate School of Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Keiji Saito

  2. Department of Physics, Gakushuin University, Mejiro, Toshima-ku, Tokyo, 171-8588, Japan

    Hal Tasaki

Authors
  1. Keiji Saito
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  2. Hal Tasaki
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Correspondence to Keiji Saito.

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Saito, K., Tasaki, H. Extended Clausius Relation and Entropy for Nonequilibrium Steady States in Heat Conducting Quantum Systems. J Stat Phys 145, 1275–1290 (2011). https://doi.org/10.1007/s10955-011-0346-0

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  • DOI: https://doi.org/10.1007/s10955-011-0346-0

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