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

TL;DR

This paper critiques a recent theoretical model for the specific heat of liquids, highlighting fundamental errors and inconsistencies that undermine its validity and applicability.

Contribution

It provides a critical analysis pointing out errors and inaccuracies in a recent theoretical approach to liquid specific heat modeling.

Findings

The proposed INM spectrum does not match known spectra of simple liquids.

The derivation from the model equation of motion contains mathematical errors.

Experimental data fitting shows the theory's inadequacy for real liquids.

Abstract

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.