Diagonality of actions and KMS weights (Q2835267)

KMS states for one-parameter groups of automorphisms of \(C^\ast\)-algebras have interpretations as equilibrium states in models of quantum statistical mechanics, and also find significant meaning in other fields including number theory and ergodic theory and dynamical systems. This paper is a contribution to the investigation of relations between properties of KMS states and properties of the one-parameter action. Building on work of \textit{S. Neshveyev} [J. Oper. Theory 70, No. 2, 513--530 (2013; Zbl 1299.46067)], it is shown here that, in the setting of a \(C^\ast\)-algebra of an étale groupoid, in many situations a one-parameter group of automorphisms is defined by a real-valued homomorphism on the groupoid if and only if the KMS weights of the one-parameter group comes from measures on the unit space. Some applications to graph \(C^\ast\)-algebras are given.