  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, the ideal gas limit and the new thermodynamic limit,
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.
