  The application of concepts from equilibrium statistical mechanics to
out-of-equilibrium systems has a long history of describing diverse systems
ranging from glasses to granular materials. For dissipative jammed systems--
particulate grains or droplets-- a key concept is to replace the energy
ensemble describing conservative systems by the volume-stress ensemble. Here,
we test the applicability of the volume-stress ensemble to describe the jamming
transition by comparing the jammed configurations obtained by dynamics with
those averaged over the ensemble as a probe of ergodicity. Agreement between
both methods suggests the idea of "thermalization" at a given angoricity and
compactivity. We elucidate the thermodynamic order of the jamming transition by
showing the absence of critical fluctuations in static observables like
pressure and volume. The approach allows to calculate observables such as the
entropy, volume, pressure, coordination number and distribution of forces to
characterize the scaling laws near the jamming transition from a statistical
mechanics viewpoint.
