Inherent structures, configurational entropy and slow glassy dynamics

We give a short introduction to the inherent structure approach to glassy systems, with particular emphasis on the Stillinger and Weber (SW) decomposition. We present some of the results obtained in the framework of spin-glass models and Lennard-Jones glasses. We discuss how to generalize the standard SW approach by including the entropy of inherent structures. Finally we discuss why this approach is probably insufficient to describe the behaviour of some kinetically constrained models