Venue: GO Jones Room 610
Physics textbooks commonly derive and discuss equations for energy and
heat capacity for gases and solids but not for liquids. Landau &
Lifshitz Statistical Physics textbook states (twice) that liquid energy
can not be calculated in general form, in contrast to solids and gases.
The reason for this was summarized by Landau as ’liquids have no small
parameter’. Here, based on the old idea of J Frenkel, I formulate the
problem in the language of phonons, and calculate liquid energy and heat
capacity for both classical and quantum cases. The resulting equation
relates heat capacity of the liquid to its relaxation time with no
fitting parameters, and is compared with the experimental data of
several liquids, including metallic, noble, molecular and network
liquids . I subsequently discuss how thermodynamic properties of the
liquid change above the critical
point using the recent idea that the mean-free path defines the minimal
wavelength of longitudinal phonons in the system and our recent finding
of the crossover of liquid specific heat in the supercritical state .
I finally discuss the new Frenkel line recently proposed to exist in the
supercritical state of matter [3,4]. Contrary to the existing view, we
have shown that the supercritical state is not physically homogeneous in
terms of its properties, but exists in two distinct states: ’rigid’
liquids and ’non-rigid’ gas-like fluids separated by a dynamic
transition across the Frenkel line on the phase diagram. All major
properties of the system, including diffusion, viscosity, thermal
conductivity, speed of sound and heat capacity as well as structure all
undergo qualitative changes at the Frenkel line, from the liquid-like to
 D. Bolmatov, V.V. Brazhkin and K. Trachenko, Sci. Rep. 2, 421 (2012).
 D. Bolmatov, V.V. Brazhkin and K. Trachenko, Nat. Comm. 4, 2331 (2013).
 V.V. Brazhkin and K. Trachenko, Physics Today 65, 68 (2012).
 V.V. Brazhkin et al., Phys. Rev. E 85, 031203 (2012); Phys. Rev.
Lett. 111, 145901 (2013).