Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States

Abstract

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.

Keywords

• lattice spin systems
• translation-invariant Gibbs measure
• concentration inequality
• relative entropy density