Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States

For a general class of lattice spin systems, we prove that an abstract Gaussian concentration bound implies positivity of the lower relative entropy density. As a consequence, we obtain uniqueness of translation-invariant Gibbs measures from the Gaussian concentration bound in this general setting....

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Detalles Bibliográficos
Autores principales: Chazottes, Jean-René, Redig, Frank
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9689258/
https://www.ncbi.nlm.nih.gov/pubmed/36359606
http://dx.doi.org/10.3390/e24111513
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author Chazottes, Jean-René
Redig, Frank
author_facet Chazottes, Jean-René
Redig, Frank
author_sort Chazottes, Jean-René
collection PubMed
description For a general class of lattice spin systems, we prove that an abstract Gaussian concentration bound implies positivity of the lower relative entropy density. As a consequence, we obtain uniqueness of translation-invariant Gibbs measures from the Gaussian concentration bound in this general setting. This extends earlier results with a different and very short proof.
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spelling pubmed-96892582022-11-25 Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States Chazottes, Jean-René Redig, Frank Entropy (Basel) Article For a general class of lattice spin systems, we prove that an abstract Gaussian concentration bound implies positivity of the lower relative entropy density. As a consequence, we obtain uniqueness of translation-invariant Gibbs measures from the Gaussian concentration bound in this general setting. This extends earlier results with a different and very short proof. MDPI 2022-10-24 /pmc/articles/PMC9689258/ /pubmed/36359606 http://dx.doi.org/10.3390/e24111513 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Chazottes, Jean-René
Redig, Frank
Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States
title Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States
title_full Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States
title_fullStr Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States
title_full_unstemmed Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States
title_short Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States
title_sort relative entropy, gaussian concentration and uniqueness of equilibrium states
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9689258/
https://www.ncbi.nlm.nih.gov/pubmed/36359606
http://dx.doi.org/10.3390/e24111513
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