  Heat capacity of matter is considered to be its most important property
because it holds information about system's degrees of freedom as well as the
regime in which the system operates, classical or quantum. Heat capacity is
well understood in gases and solids but not in the third state of matter,
liquids, and is not discussed in physics textbooks as a result. The perceived
difficulty is that interactions in a liquid are both strong and
system-specific, implying that the energy strongly depends on the liquid type
and that, therefore, liquid energy can not be calculated in general form. Here,
we develop a phonon theory of liquids where this problem is avoided. The theory
covers both classical and quantum regimes. We demonstrate good agreement of
calculated and experimental heat capacity of 21 liquids, including noble,
metallic, molecular and hydrogen-bonded network liquids in a wide range of
temperature and pressure.
