Universal empirical scaling of low-temperature heat capacity van Hove signature in classical and quantum cryocrystals.

We analyze the low-temperature isochoric heat capacity of a broad set of cryocrystals and show that the hump in the Debye-reduced function [Formula: see text], which originates from the first van Hove singularity of the phonon spectrum, can be captured within a single universal description. Specifically, we demonstrate that the hump is reproduced by a dimensionless function [Formula: see text] that depends only on the magnitude of the feature and the characteristic temperature [Formula: see text], without requiring a system-specific model beyond the standard behavior of the phonon density of states near a van Hove maximum. Across atomic (Ar, Ne, Kr, Xe), molecular (N[Formula: see text], CO, CO[Formula: see text], N[Formula: see text]O), and quantum ([Formula: see text]He, [Formula: see text]He, H[Formula: see text]) crystals, we find that [Formula: see text] scales with molar volume in a manner consistent with Brillouin-zone scaling of the corresponding phonon frequencies. Even in quantum solids - where zero-point motion strongly modifies lattice dynamics - the proportional relations among [Formula: see text], the peak value [Formula: see text], and the Debye heat capacity remain reliable and systematic. These results show that [Formula: see text] provides a compact and practical framework for organizing low-temperature heat capacity data of diverse cryocrystals. The approach does not introduce new physics beyond established lattice dynamics; rather, it highlights a simple and previously unrecognized universality in how van Hove - related features of the phonon spectrum appear in thermodynamic observables.