Supercritical Gr\"uneisen parameter and its universality at the Frenkel line

We study thermo-mechanical properties of matter at extreme conditions deep in the supercritical state, at temperatures exceeding the critical one up to four orders of magnitude. We calculate the Gr\"{u}neisen parameter {\gamma} and find that it decreases with temperature from 3 to 1 on isochores depending on the density. Our results indicate that from the perspective of thermo-mechanical properties, the supercritical state is characterized by the wide range of {\gamma} which includes the solid-like 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 {\gamma} is nearly constant at the Frenkel line above the critical point and explain this universality in terms of pressure and temperature scaling of system properties along the lines where particle dynamics changes qualitatively.