Comment on "Explaining the specific heat of liquids based on instantaneous normal modes"

In a recent paper [Phys. Rev. E 104, 014103 (2021)10.1103/PhysRevE.104.014103] Baggioli and Zaccone formulate a theoretical description of the specific heat of liquids by using Debye's expression for the specific heat of solids and inserting a density of states which they claim to represent the instantaneous-normal-mode (INM) spectrum of a liquid. However, the quantum-mechanical procedure of Debye cannot be used for the relaxational excitations of a classical liquid. Furthermore, the authors' formula for the INM spectrum does not represent the known INM spectra of simple liquids, and the derivation of this formula from their model equation of motion is mathematically in error. These and a number of other inconsistencies render their work not very helpful for studying the specific heat of liquids.