  We consider operator-algebraic dynamical systems given by actions of the real
line on unital $C^*$-algebras, and especially the equilibrium states (or KMS
states) of such systems. We are particularly interested in systems built from
the gauge action on the Toeplitz algebra and graph algebra of a finite directed
graph, and we describe a complete classification of the KMS states obtained in
joint work with Laca and Sims. We then discuss applications of these results to
Cuntz-Pimsner algebras associated to local homeomorphisms, obtained in
collaboration with Afsar. Thomsen has given bounds on the range of inverse
temperatures at which KMS states may exist. We show that Thomsen's bounds are
sharp.
