1. Levich Institute and Physics Department, City College of the City University of New York, New York, New York 10031, USA
2. PMMH, Ecole Supérieure de Physique et Chimie Industrielles, 10 rue Vauquelin, 75231 Paris, France

Correspondence to: Hernán A. Makse¹ Correspondence and requests for materials should be addressed to H.A.M. (e-mail: Email: makse@mailaps.org).

Edwards has proposed^{1, 2, 3} a thermodynamic description of dense, slowly flowing granular matter, in which the grains (the 'atoms' of the system) interact with inelastic forces and enduring contacts. In Edwards' ensemble—one of the very few generalizations of standard statistical mechanics—thermodynamic quantities are computed as flat averages over configurations in which the grains are static or jammed, leading to a natural definition of configurational temperature. But the approach is not justified from first principles and hence, in the absence of explicit tests of its validity, has not been widely accepted. Here we report a numerical experiment involving a realistic model of slowly sheared granular matter; our results strongly support the thermodynamic description. Considering particles of different sizes in a slowly sheared dense granular system, we extract an effective temperature from a relation connecting their diffusivity and mobility. We then perform an explicit computation to show that the effective temperature measured from this relation coincides with the Edwards configurational temperature. Our approach, which is specifically conceived to be reproducible in the laboratory, may thus render the Edwards temperature accessible to experiments.