  We consider Pimsner algebras that arise from C*-correspondences of finite
rank, as dynamical systems with their rotational action. We revisit the
Laca-Neshveyev classification of their equilibrium states at positive inverse
temperature along with the parametrizations of the finite and the infinite
parts simplices by tracial states on the diagonal. The finite rank entails an
entropy theory that shapes the KMS-structure. We prove that the infimum of the
tracial entropies dictates the critical inverse temperature, below which there
are no equilibrium states for all Pimsner algebras. We view the latter as the
entropy of the ambient C*-correspondence. This may differ from what we call
strong entropy, above which there are no equilibrium states of infinite type.
In particular, when the diagonal is abelian then the strong entropy is a
maximum critical temperature for those. In this sense we complete the
parametrization method of Laca-Raeburn and unify a number of examples in the
literature.
