  We investigate the nature of randomness in disordered packings of frictional
spheres. We calculate the entropy of 3D packings through the force and volume
ensemble of jammed matter, a mesoscopic ensemble and numerical simulations
using volume fluctuation analysis and graph theoretical methods. Equations of
state are obtained relating entropy, volume fraction and compactivity
characterizing the different states of jammed matter. At the mesoscopic level
the entropy vanishes at random close packing. The entropy of the jammed system
reveals that the random loose packings are more disordered than random close
packings, allowing for an unambiguous interpretation of both limits.
