Equivalence of Fluctuation-Dissipation and Edwards’ Temperature in Cyclically Sheared Granular Systems

Abstract

Using particle trajectory data obtained from x-ray tomography, we determine two kinds of effective temperatures in a cyclically sheared granular system. The first one is obtained from the fluctuation-dissipation theorem which relates the diffusion and mobility of lighter tracer particles immersed in the system. The second is the Edwards compactivity defined via the packing volume fluctuations. We find robust agreement between these two temperatures, independent of the type of the tracers, cyclic shear amplitudes, and particle surface roughness, giving therefore the first experimental evidence that the concept of effective temperature is valid in driven frictional granular systems.