Physical quantities that characterize a macroscopic system can be in principle calculated averaging over all the microscopic states the system can reach. The probability distribution related to these states is known to be the Gibbs-Boltzmann one if the system is at equilibrium. The description of out-of-equilibrium systems is actually more complicated because a general expression of the probability measure is not known at present.

Glassy systems (structural glasses, disordered systems) are by definition out-of-equilibrium systems because their relaxation toward equilibrium takes place in a time abnormally long with respect to experimental time-scales. Furthermore, their phenomenology is such varied (absence of stationary states, aging, dynamical heterogeneities), that it can be described only from a dynamical point of view.

The thermodynamic formalism of « histories » built-up by Ruelle and coworkers is based on the construction of a dynamical partition function which is the analog for trajectories of the canonical partition function for microscopic states in the equilibrium thermodynamics. The aim of this PhD is to utilize this formalism to properly describe glassy systems.

Works in progress:

To portray the glassy behaviour we consider kinetically constrained models (KCM). We apply numerically the thermodynamic formalism to the Triangular Lattice Gas Model (TLG), and to the Kob-Andersen model in two dimensions ; in both cases we observe a dynamical transition in the space of histories.

We try as well to apply analytically the thermodynamic formalism to disordered systems like the Random Energy Model (R.E.M) and the Directed Trap Model.

Publication :

Dynamic first-order transition in kinetically constrained models of glasses (submitted).

J.P. Garrahan, R.L. Jack, V. Lecomte, E. Pitard, K. van Duijvendijk and F. van Wijland.

[cond-mat/0701757]