Fig. 1. Ensemble calculations. The density of states g (Γ , φ ) as a function of internal virial Γ for different volume fraction, φ , ranging from 0.610 to 0.670. The inset is a schematic two-dimensional potential energy landscape surface. The jammed states A and B are local minima (zero order saddles) in the PES where the external force for each particle is zero and the Hessian matrix of the system is positive definite. Our simulation system consists of 30 frictionless spherical particles interacting by Hertzian forces with periodic boundary conditions. Fig. 2. Scaling of pressure and inverse angoricity. (A) The blue ○ shows the power-law relation for 〈 p 〉 dyn vs 〈 φ 〉 dyn − φ$_{c}$ for the 30-particle system. Here, the pressure 〈 p 〉 dyn are average values obtained by 250 independent MD simulations. The red ○ is the pressure used to obtain the inverse angoricity α predicted by Eq. (4). The relatively small system size results in large fluctuations of the observables. In order to predict a precise relation for the system ( N = 30), sufficient independent samples of the packings are generated to calculate the precise average for observables. We prepare 250 independent packings for each φ to get enough statistical samples to obtain 〈 p 〉 dyn and 〈 Z 〉 dyn by statistical average (see Fig. 8). The inset shows a semi-log plot. (B) The inverse angoricity α as a function of φ - φ$_{c}$ . We find a power-law relation for system’s volume fraction φ near φ$_{c}$ . The solid line has a slope of -2.5. The inset is the angoricity A (= 1 /α ) vs φ - φ$_{c}$ . The plateau observed in A for large volume fraction φ might be related to the finite size of the sample. Fig. 3. Test of ergodicity. (A) The blue ○ is the average coordination number 〈 Z 〉 dyn obtained by 250 independent MD simulations. The red ○ is the coordination number 〈 Z 〉 ens calculated by the ensemble for different volume fractions. Agreement between both measures supports the concept of ergodicity in the system. (B) The same as (A) but in a log-log plot. The blue ○ shows the power-law relations for 〈 Z 〉 $_{dyn}$- Z$_{c}$ vs 〈 φ 〉 dyn - φ$_{c}$ for 30-particle system with φ$_{c}$ = 0 . 6077 and Z$_{c}$ = 5 . 82. (C) Comparison of 〈 F 〉 dyn and 〈 F 〉 ens for different volume fractions. (D) The comparison of selected distributions of forces P$_{dyn}$ ( F/F ) and P$_{ens}$ ( F/F ) for different volume fractions. Fig. 4. Microcanonical calculations. The entropy surface S (ln( φ − φ$_{c}$ ) , ln p ). The color bar indicates the value of the entropy. The superimposed blue ○ is 〈 p ( φ ) 〉 dyn from MD calculations as in Fig. 2a. The olive arrow line indicates the maximization direction of the entropy ( − sin θ, cos θ ). Following this direction, the entropy is maximum at the point (ln( 〈 φ 〉 dyn − φ$_{c}$ ) , ln 〈 p 〉 $_{dyn}$), corroborating the maximum entropy principle. 17