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.

中文翻译：

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Pimsner 代数平衡态参数化的熵理论

我们将源自有限秩的 C*-对应关系的 Pimsner 代数视为具有旋转作用的动力系统。我们重新审视了它们在正逆温度下的平衡状态的 Laca-Neshveyev 分类，以及对角线上轨迹状态的有限和无限部分单纯形的参数化。有限秩需要一个塑造 KMS 结构的熵理论。我们证明轨迹熵的下界决定了临界逆温度，低于该温度时，所有 Pimsner 代数都没有平衡态。我们将后者视为环境 C* 对应的熵。这可能与我们所说的强熵不同，在强熵之上没有无限类型的平衡状态。特别是，当对角线是阿贝尔时，强熵是那些的最大临界温度。在这个意义上，我们完成了 Laca-Raeburn 的参数化方法，并统一了文献中的一些例子。