  In a recent paper (Phys. Rev. E {\bf 104}, 014103 (2021) ) M. Baggioli and A.
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 (DOS) 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 a classical liquid and
the authors' formula for the INM spectrum does not represent the known INM
spectra of simple liquids. Furthermore, the derivation of this formula from
their model equation of motion is mathematically in error. Finally experimental
test of the teory for the specific heat of {\it liquids} is performed by
fitting the data of {\it supercritical fluids}. \new{To our opinion,} these and
a lot of other inconsistencies render this work not suitable for studying the
specific heat of liquids.
