Journal of Symplectic Geometry

Volume 21 (2023)

Number 5

Classical KMS functionals and phase transitions in Poisson geometry

Pages: 939 – 995

DOI: https://dx.doi.org/10.4310/JSG.2023.v21.n5.a3

Authors

Nicolò Drago (Dipartimento di Matematica, Università di Trento, Povo, Italy)

Stefan Waldmann (Department of Mathematics, Julius Maximilian University, Würzburg, Germany)

Abstract

In this paper 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 their 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.

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Received 15 September 2021

Received revised 16 December 2022

Accepted 18 October 2022

Published 4 June 2024