Inherent structures and non-equilibrium dynamics of 1D constrained kinetic models: a comparison study

e discuss the relevance of the Stillinger and Weber approach to the glass transition investigating the non-equilibrium behavior of models with non-trivial dynamics, but with simple equilibrium properties. We consider a family of 1D constrained kinetic models, which interpolates between the asymmetric chain introduced by Eisinger and J\"ackle [Z. Phys. {\bf B84}, 115 (1991)] and the symmetric chain introduced by Fredrickson and Andersen [Phys. Rev. Lett {\bf 53}, 1244 (1984)], and the 1D version of the Backgammon model [Phys. Rev. Lett. {\bf 75}, 1190 (1995)]. We show that the configurational entropy obtained from the inherent structures is the same for all models irrespective of their different microscopic dynamics. We present a detailed study of the coarsening behavior of these models, including the relation between fluctuations and response. Our results suggest that any approach to the glass transition inspired by mean-field ideas and resting on the definition of a configurational entropy must rely on the absence of any growing characteristic coarsening pattern.