A consequence of local equilibration and heterogeneity in glassy materials

The existence of a generalized fluctuation–dissipation theorem observed in simulations and experiments performed in various glassy materials is related to the concepts of local equilibration and heterogeneity in space. Assuming the existence of a dynamic coherence length scale up to which the system is locally equilibrated, we extend previous generalizations of the FDT relating static to dynamic quantities to the physically relevant domain where asymptotic limits of large times and sizes are not reached. The formulation relies on a simple scaling argument and thus does not have the character of a theorem. Extensive numerical simulations support this proposition. Our results quite generally apply to systems with slow dynamics, independently of the space dimensionality, the chosen dynamics or the presence of disorder. PACS numbers: 05.70.Ln, 75.10.Nr, 75.40.Mg How slow the wind How slow the sea E Dickinson Materials can be far from their equilibrium state for two main reasons. First, the relaxation time can be very large compared to the experimental time scale and the system does not reach equilibrium. This is typically the case for a liquid supercooled through its melting transition below its glass transition. The glass state is thus a non-stationary non-equilibrium state, where the glass is said to age. ‘Glass phases’ are extremely commonly encountered in condensed matter [1]. Secondly, when some external drive mechanism is applied to the system, it also leaves its equilibrium state. Typical situations can be driven interfaces, or soft materials perturbed by a mechanical flow. In this paper, we consider these two types of situations in the specific case of systems with slow dynamics. We discuss theoretically and numerically the existence and formulation of a generalization of the equilibrium fluctuation–dissipation theorem and its link to equilibrium properties. 0305-4470/03/4310667+15$30.00 © 2003 IOP Publishing Ltd Printed in the UK 10667