QHA beyond just phonopy

The beautiful thing about quasi-harmonic approximation is that it follows the basic thermodynamic principle within the harmonic range, i.e. the thermodynamic state is a manifold of two natural variables, which are:

• $T$, $V$ for Helmholtz free energy $F$
• $T$, $p$ for Gibbs free energy $G$.

All derivative quantities, whether it's heat capacity ($T$ and $V$ or $T$ and $p$) or thermal expansion ($T$ and $p$) follow the same principle. That's the real beauty of my Thermodynamics class. Currently, I see that the QHA class here is a very pragmatic implementation, but If we want to go beyond just phonopy and be able to describe the full thermodynamics we should definitely follow the same pattern.

Right now I'm too busy, but I will try to implement this aspect over Christmas.