Angoricity and compactivity describe the jamming transition in soft particulate matter Kun Wang $^{1}$, Chaoming Song$^{2}$, Ping Wang$^{3}$, Hern´an A. Makse1 $^{1}$Levich Institute and Physics Department, City College of New York, New York, NY 10031, US $^{2}$Center for Complex Network Research, Department of Physics, Biology and Computer Science, Northeastern University, Boston, MA 02115, US $^{3}$FAS Center for Systems Biology, Harvard University, Cambridge, MA 02138, US (Dated: September 11, 2018) 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 en- ergy 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 num- ber and distribution of forces to characterize the scaling laws near the jamming transition from a statistical mechanics viewpoint. 1 arXiv:1001.5295v2 [cond-mat.soft] 28 Mar 2016 Abstract