Edwards measure and the steady state regime of a model with kinetic constraints under tapping

We study the tapping dynamics of a one dimensional Ising model with symmetric kinetic constraints. We define and test a variant of the Edwards hypothesis that one may build a thermodynamics for the steady state by using a flat measure over the metastable states with several macroscopic quantities fixed. Various types of tapping are compared and the accuracy of this measure becomes quickly excellent when the number of quantities fixed on average increases, independently of the way the system is excited. We attribute the validity of the naive flat measure at weak tapping to the spatial separation of density defects.