Dynamic phase transitions in model glass formers*

Glassy dynamics is identified through a series of signatures, such as aging, slow relaxation and the presence of dynamical heterogeneities. Basing our considerations on kinetically constrained glass formers, we argue that these phenomena are the byproduct of an intrinsically dynamic phase transition. The latter can be unravelled by performing, in the spirit of Ruelle, a Gibbs-like statistical mechanics over the set of time realizations of the systems' evolution, rather than over the conventional set of phase space configurations.