Unified phonon-based approach to the thermodynamics of solid, liquid and gas states

We introduce a unified approach to states of matter (solid, liquid and gas) and describe the thermodynamics of the pressure-temperature phase diagram in terms of phonon excitations. We derive the effective Hamiltonian with low-energy cutoff in two transverse phonon polarizations (phononic band gaps) by breaking the symmetry in phonon interactions. Further, we construct the statistical mechanics of states of aggregation employing the Debye approximation. The introduced formalism covers the Debye theory of solids, the phonon theory of liquids, and thermodynamic limits such as the Dulong-Petit thermodynamic limit (cV=3kB), the ideal gas limit (cV=32kB) and the new thermodynamic limit (cV=2kB), dubbed here the Frenkel line thermodynamic limit. We discuss the phonon propagation and localization effects in liquids above and below the Frenkel line, and explain the “fast sound” phenomenon. As a test for our theory we calculate velocity-velocity autocorrelation and pair distribution functions within the Green-Kubo formalism. We show the consistency between dynamics of phonons and pair correlations in the framework of the unified approach. New directions towards advancements in phononic band gaps engineering, hypersound manipulation technologies and exploration of exotic behaviour of fluids relevant to geo- and planetary sciences are discussed. The presented results are equally important both for practical implications and for fundamental research.