  The thermodynamics of liquids and supercritical fluids is notorious for
eluding a general theory, as can be done for crystalline solids on the basis of
phonons and crystal symmetry. The extension of solid state notions such as
configurational entropy and phonons to the liquid state remains an intriguing
but challenging topic. This is particularly true for liquids like water whose
many structural anomalies give it unique properties. Here, for simple fluids,
we specify the thermodynamics across the liquid, supercritical, and gaseous
states using the spectrum of propagating phonons, thereby determining the
non-ideal entropy of the fluid using a single parameter arising from this
phonon spectrum. This identifies a marked distinction between these "simple"
fluids, and hydrogen bonded fluids whose non-ideal entropy cannot be determined
by the phonon spectrum alone. We relate this phonon theory of thermodynamics to
the previously observed excess entropy scaling in liquids and how the phonon
spectrum creates corresponding states across the fluid phase diagram. These
results provide important theoretical understanding to supercritical fluid,
whose properties are still poorly understood despite widespread deployment in
environmental and energy applications.
