English

Gibbs variational formula for thermal equilibrium states in terms of quantum relative entropy density

Mathematical Physics 2022-05-27 v4 math.MP

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 F\"ollmer for classical systems. In this work we advocate the viewpoint: Avoid the unique-phase assumption if it is not essential.

Keywords

Cite

@article{arxiv.2002.04253,
  title  = {Gibbs variational formula for thermal equilibrium states in terms of quantum relative entropy density},
  author = {Hajime Moriya},
  journal= {arXiv preprint arXiv:2002.04253},
  year   = {2022}
}

Comments

Eq (31) (32) are incorrect. Hence the given statements are not proved