can be distributed in a given volume. Since the stresses have a unique solution for a given configuration at the isostatic point, φ$_{c}$ , the corresponding angoricity vanishes. At higher pressure, the system is determined by multiple degrees of freedom satisfying mechanical equilibrium, leading to a higher stress temperature, A . The angoricity can also be viewed as a scale of stability for the system at different volume fractions. Systems jammed at larger volume fractions require higher angoricity (higher driving force) to rearrange. Test of ergodicity.— In principle, using the inverse angoricity, α , from Eq. (5) we can calculate any macroscopic statistical observable 〈 B 〉 ens at a given volume by performing the ensemble average [10]: We test the ergodic hypothesis in the Edwards’s ensemble by comparing Eq. (6) with the corresponding value obtained with MD simulations averaged over (250) sample packings, B$_{i}$ , generated dynamically: The comparison is realized by measuring the average coordination number, 〈 Z 〉 , the average force and the distribution of interparticle forces. We calculate 〈 Z 〉 ens by Eq. (2) and 〈 Z 〉 dyn as in Eq. (7). Figures 3A and 3B show that the two independent estimations of the coordination number agree very well: 〈 Z 〉 ens = 〈 Z 〉 $_{dyn}$. We calculate the ensemble average force 〈 F 〉 ens and the average over all the MD packings, 〈 F 〉 dyn and find that they coincide very closely (see Fig. 3C). The full distribution of inter-particle forces for jammed systems is also an important observable which has been extensively studied in previous works [4, 25, 26]. The force distribution is calculated in the ensemble P$_{ens}$ ( F/F ) by averaging the force distribution for every configuration in the PES (see Materials and Methods Section III D). Figure 3D shows the distribution functions. The peak of the distribution shown in Fig. 3D indicates that the systems are jammed [4, 25, 26]. Besides the exact shape of the distribution, the similarity between the ensemble and the dynamical calculations shown in Fig. 3D is significant. The study of 〈 Z 〉 , 〈 F 〉 and P ( F/F ) reveals that the statistical ensemble can predict the macroscopic observables obtained in MD. This suggests that the idea of “thermalization” at an angoricity is able to describe the jamming system very well. 5 〈 B ( φ ) 〉 dyn = 1 250 250 ∑ i =1 B$_{i}$. (7) 〈 B ( φ ) 〉 ens = 1 Z ∫ ∞ 0 B g (Γ , φ ) e − α Γ dΓ . (6)