A proof of the equivalence of ensembles for asymptotically decoupled fields relying on Mosco's theorem

TL;DR

This paper proves the equivalence of entropy and the Fenchel-Legendre transform of pressure for asymptotically decoupled fields using Mosco's theorem, providing a rigorous mathematical foundation for this identification.

Contribution

It introduces a novel proof of the entropy-pressure relationship for asymptotically decoupled fields based on Mosco's theorem, extending theoretical understanding.

Findings

Established the entropy and pressure transform equivalence for asymptotically decoupled fields.

Utilized Mosco's theorem to rigorously prove the identification.

Provided a new mathematical framework for analyzing such fields.

Abstract

We give a proof of the identification between the entropy and the opposite of the Fenchel-Legendre transform of the pressure for asymptotically decoupled fields relying on Mosco's theorem. ----- Nous d\'emontrons l'identification entre l'entropie et l'oppos\'ee de la transform\'ee de Fenchel-Legendre de la pression pour les champs asymptotiquement d\'ecoupl\'es \`a partir du th\'eor\`eme de Mosco.