We develop an approach to liquid thermodynamics based on collective modes. We perform extensive molecular-dynamics simulations of noble, molecular, and metallic liquids, and we provide direct evidence that liquid energy and specific heat are well-described by the temperature dependence of the Frenkel (hopping) frequency. The agreement between predicted and calculated thermodynamic properties is seen in the notably wide range of temperature spanning tens of thousands of Kelvin. The range includes both subcritical liquids and supercritical fluids. We discuss the structural crossover and interrelationships between the structure, dynamics, and thermodynamics of liquids and supercritical fluids.

Physical properties of an interacting system are governed by collective excitations, but their nature at extreme supercritical conditions is unknown. Here, we present direct evidence for propagating solid-like longitudinal phonon-like excitations with wavelengths extending to interatomic separations deep in the supercritical state at temperatures up to 3,300 times the critical temperature. We observe that the crossover of dispersion curves develops at k points reducing with temperature. We interpret this effect as the crossover from the collective phonon to the collisional mean-free path regime of particle dynamics and find that the crossover points are close to both the inverse of the shortest available wavelength in the system and to the particle mean free path inferred from experiments and theory. Notably, both the shortest wavelength and mean free path scale with temperature with the same power law, lending further support to our findings.

We study the thermomechanical properties of matter under extreme conditions deep in the supercritical state, at temperatures exceeding the critical one by up to four orders of magnitude. We calculate the Grüneisen parameter γ and find that on isochores it decreases with temperature from 3 to 1, depending on the density. Our results indicate that from the perspective of thermomechanical properties, the supercritical state is characterized by a wide range of γ's which includes solidlike values-an interesting finding in view of the common perception of the supercritical state as being an intermediate state between gases and liquids. We rationalize this result by considering the relative weights of oscillatory and diffusive components of the supercritical system below the Frenkel line. We also find that γ is nearly constant at the Frenkel line above the critical point and explain this universality in terms of the pressure and temperature scaling of system properties along the lines where particle dynamics changes qualitatively.

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