Configurational entropy and the one - step RSB scenario in glasses

In this talk we discuss the possibility of constructing a fluctuation theory for structural glasses in the non-equilibrium aging state. After reviewing well known results in a toy model we discuss some of the key assumptions which support the validity of this theory, in particular the role of the configurational entropy and its relation to the effective temperature. Recent numerical results for mean-field finite-size glasses agree with this scenario. A theoretical understanding of the physical mechanisms behind the glass transition remains an open problem [1]. What is commonly understood as a glass (for instance, window glass) is a metastable phase, with free energy higher than that of the crystal obtained by the continuation of the liquid line below the melting transition temperature T M. Such a glassy state may be experimentally achieved by cooling the liquid fast enough. Glasses share physical properties common to liquids and solids making difficult to decide in which phase (if any) their are. On the one hand, atom positions are randomly located in the glass much alike a liquid and apparently there is no long-range order. On the other hand, under compression glasses behave like a solid showing a very low mobility. Glasses constitute a state of matter in between liquids and solids, not completely classificable as any of them, which show the following generic features: • The viscosity anomaly. Glasses show a very rapid increase of the viscosity η in a relatively narrow range of temperatures. For instance, in window glass the viscosity increases over nearly 20 orders of magnitude by changing the temperature in a range within a 10% of the value of the melting transition temperature. This increase is often well fitted by the Vogel-Tamman-Fulcher law, η ∼ exp(∆/(T − T 0)) where T 0 and ∆ are free parameters. Fragile glasses