Motivated by the study of the metastable stochastic Ising model at subcritical temperature and in the limit of a vanishing magnetic field, we extend the notion of (kappa, lambda)-capacities between sets, as well as the associated notion of soft-measures, to the case of overlapping sets. We recover their essentials properties, sometimes in a stronger form or in a simpler way, relying on weaker hypotheses. These properties allow to write the main quantities associated with reversible metastable dynamics, e.g. asymptotic transition and relaxation time, in terms of objects satisfying two-sided variational principles. We also make the connection with the classical "pathwise approach".

中文翻译：

---

关于软电容、准平稳分布和亚稳态的路径方法

受亚临界温度和消失磁场限制下的亚稳态随机 Ising 模型的研究的启发，我们将 (kappa, lambda)-组间容量的概念以及相关的软测量概念扩展到重叠集的情况。我们依赖较弱的假设，有时以更强的形式或更简单的方式恢复它们的基本属性。这些属性允许根据满足两侧变分原理的对象来写出与可逆亚稳态动力学相关的主要量，例如渐近跃迁和弛豫时间。我们还与经典的“路径方法”建立了联系。