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The jamming transition of non-spherical particles is fundamentally differentfrom the spherical case. Non-spherical particles are hypostatic at theirjamming points, while isostaticity is ensured in the case of the jamming ofspherical particles. This structural difference implies that the presence ofasphericity affects the critical exponents related to the contact number andthe vibrational density of states. Moreover, while the force and gapdistributions of isostatic jamming present power-law behaviors, even aninfinitesimal asphericity is enough to smooth out these singularities. In arecent work [PNAS 115(46), 11736], we have used a combination of marginalstability arguments and the replica method to explain these observations. Weargued that systems with internal degrees of freedom, like the rotations inellipsoids, or the variation of the radii in the case of the \textit{breathing}particles fall in the same universality class. In this paper, we reviewcomprehensively the results about the jamming with internal degrees of freedomin addition to the translational degrees of freedom. We use a variationalargument to derive the critical exponents of the contact number, shear modulus,and the characteristic frequencies of the density of states. Moreover, wepresent additional numerical data supporting the theoretical results, whichwere not shown in the previous work.

Infinitesimal asphericity changes the universality of the jamming transition