Classical KMS Functionals and Phase Transitions in Poisson Geometry

TL;DR

This paper investigates the structure of KMS measures in Poisson geometry, especially on $b$-Poisson manifolds, extending classical results and exploring phase transition phenomena.

Contribution

It generalizes the theory of KMS measures from smooth to non-smooth contexts in Poisson geometry, with a focus on $b$-Poisson manifolds, providing a near-complete characterization.

Findings

Characterization of KMS measures on $b$-Poisson manifolds

Extension of classical KMS theory to non-smooth measures

Insights into phase transitions in Poisson geometric settings

Abstract

We study the convex cone of not necessarily smooth measures satisfying the classical KMS condition within the context of Poisson geometry. We discuss the general properties of KMS measures and its relation with the underlying Poisson geometry in analogy to Weinstein's seminal work in the smooth case. Moreover, by generalizing results from the symplectic case, we focus on the case of $b$-Poisson manifolds, where we provide an almost complete characterization of the convex cone of KMS measures.