An alternative approach to the phonon theory of liquids: the evolution of the energy of diffusion

With regard to the three basic states of matter (solid, liquid and gas), the calculation of the heat capacity of liquids in a general form has been considered one of the deepest and most interesting challenges in condensed matter physics, due to the strong, system-specific interactions involved. Notwithstanding the theoretical difficulties, there have recently been significant advances in our understanding of liquids, and the phonon theory of liquids has been proposed. However, this theory uses the virial theorem to calculate the liquid energy. Here, we propose an alternative version of the phonon theory of liquids by taking into account the numbers of oscillating atoms and diffusing atoms, rather than using the virial theorem. A new formula is derived for the liquid energy in both the quantum and the classical anharmonic cases. To verify the proposed approach, theoretical predictions are compared with the experimental specific heat of liquid mercury. Finally, we obtain a new expression for the energy of a supercritical system.