Metastability and aging are phenomenoma appearing in (stochastic) dynamical systems that are seriously out of equilibrium. In about the year 2000, with Michael Eckhoff, Veronique Gayrard, and Markus Klein. we developed a new approach to this subject that by now is called the "potential-theoretic approach to metastability".
There is now a rather feisty book I wrote with Frank den Hollander on this subject. It gives a fairly comprehensive account of the potential theoretic approach to metastability and should supersed all previous lecture notes. The book is published by Springer as Vol. 351 of the series Grundlehren der mathematischen Wissenschaften.