Abstract. We give a short introduction to the inherent structure approach, with particular emphasis on the Stillinger and Weber decomposition, of glassy systems. 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 Stillinger and Weber approach by including the entropy of inherent structures. Finally we discuss why this approach is probably insufficient to describe the behavior of some kinetically constrained models. PACS numbers: 64.70.Pf, 75.10.Nr, 61.20.Gy, 82.20.WtInherent Structures, Configurational Entropy and Slow Glassy Dynamics
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