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Gibbs Variational Formula for Thermal Equilibrium States in Terms of Quantum Relative Entropy Density

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Abstract

We prove the Gibbs variational formula in terms of quantum relative entropy density that characterizes translation invariant thermal equilibrium states in quantum lattice systems. It is a natural quantum extension of the similar statement established by Föllmer for classical systems.

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Acknowledgements

I would like to thank Prof. Toshiyuki Toyoda for discussion on interplay between physics and information. Prof. Dénes Petz and Prof. Fumio Hiai told me their fundamental ideas of [5]. In particular, Prof. Hiai kindly sent me his private note explaining mathematical details.

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Authors and Affiliations

  1. College of Science and Engineering, Kanazawa University, Kanazawa, Japan

    Hajime Moriya

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  1. Hajime Moriya
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Correspondence to Hajime Moriya.

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Communicated by Eric A. Carlen.

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Moriya, H. Gibbs Variational Formula for Thermal Equilibrium States in Terms of Quantum Relative Entropy Density. J Stat Phys 181, 761–771 (2020). https://doi.org/10.1007/s10955-020-02600-5

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