Edwards' measures: A thermodynamic construction for dense granular media and glasses

We present numerical support for the hypothesis that macroscopic observables of dense granular media and glasses can be evaluated from averages over typical blocked configurations: we construct the corresponding measure for a class of finite-dimensional systems and compare its predictions for various observables with the outcome of the out of equilibrium dynamics at large times. We discuss in detail the connection with the effective temperatures that appear in out of equilibrium glass theories, as well as the relation between our computation and those based on "inherent structure" arguments. A short version of this work has appeared in Phys. Rev. Lett. 85, 5034 (2000).