Extended Clausius Relation and Entropy for Nonequilibrium Steady States in Heat Conducting Quantum Systems |
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Authors: | Keiji Saito Hal Tasaki |
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Institution: | 1.Graduate School of Science,University of Tokyo,Tokyo,Japan;2.Department of Physics,Gakushuin University,Tokyo,Japan |
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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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