C. Relation to the glass transition III. DESCRIPTIVE VIEWPOINT OF THE RCP TRANSITION A. Orientational order parameter 21 The thermodynamic character of the RCP transition seemingly contrasts to the non- thermodynamic viewpoint of the glass transition which proposes a dynamical arrest upon supercooling [17]. However, the same phenomenology of vitrification could be applied to the RCP transition by extrapolating the entropy of the disordered branch s ( φ$_{j}$ ) into a metastable region below the freezing point as schematically shown in Figs. 1 and 3B from a → b . Two scenarios may emerge: the metastable branch may end in a metastability limit at the spinodal ∂X/∂S = 0 [17] or it may continue until the entropy of the metastable liquid is zero as shown in Fig. 3B. Such a scenario would predict a Kauzmann density φ$_{K}$ at which the entropy of the disordered branch vanishes, signaling the existence of an ideal jammed glass analogous to the Kauzmann temperature in glasses [6]. The orientational order is measured by associating a set of spherical harmonics with every bond joining a sphere and its neighbors [19]: where the { Y$_{lm}$ ( θ, φ ) } are spherical harmonics, and θ ( ⃗ r ) and φ ( ⃗ r ) are the polar angles of the bond. The local orientational order parameter q$_{l}$ for a particle i is given by rotationally invariant combinations of Q$_{lm}$ , where Q$_{lm,i}$ is averaged over N$_{i}$ neighbors of this particle, We also consider the global orientational order Q$_{l}$ , as well as the third-order invariants W$_{l}$ , which are Q$_{lm}$ ( ⃗ r ) = Y$_{lm}$ ( θ ( ⃗ r ) , φ ( ⃗ r )) , (6) q$_{l}$ = [ 4 π 2 l + 1 l ∑ m = − l ∣ Q$_{lm,i}$ ∣ ∣$^{2}$ ] 1 / 2 , (7) Q$_{lm,i}$ = 1 N$_{i}$ N$_{i}$ ∑ j =1 Q$_{lm}$ ( ⃗ r$_{ij}$ ) . (8)