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

We reply to the Comment by Schirmacher et al. [Phys. Rev. E, 106, 066101 (2022)PREHBM2470-004510.1103/PhysRevE.106.066101]. We disagree that the heat capacity of liquids is not a mystery since a widely accepted theoretical derivation based on simple physical assumptions is still missing. We also disagree about the lack of evidence for a linear in frequency scaling of the liquid density of states, which is indeed reported in uncountable simulations and recently also in experiments. We emphasize that our theoretical derivation does not assume any Debye density of states. We agree that such an assumption would be incorrect. Finally, we remark that the Bose-Einstein distribution naturally tends to the Boltzmann distribution in the classical limit, which makes our results valid also for classical liquids. We hope that this scientific exchange will bring more attention to the description of the vibrational density of states and thermodynamics of liquids, which still present many open puzzles.