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The rigorous Equation of State of any material under external isotropic pressure $P$:
$ \hspace{2.5cm} P =\frac {1}{\beta} \frac {\partial \ln Z}{\partial V}, $
based on the system partition function $Z$, is taught in almost every related textbook.
The Equation of State of crystals under general external stress $\mathbf{S}$ was derived:
$ \hspace{2.5cm} \mathbf{S} \cdot \mathbf{\sigma}_{\mathbf{h}}=-\frac {1}{\beta} \frac {\partial \ln Z}{\partial \mathbf{h}} \ \ \ (\mathbf{h}=\mathbf{a}, \mathbf{b}, \mathbf{c}), $
with respect to the crystal period vectors $\mathbf{h}$, in our recent article:
https://doi.org/10.1140/epjp/s13360-020-01010-6
which has been accessed about 23,000 times.
Here, we also derived the Equation of State of non-crystals under external stress and temperature and studied its relationship with the macroscopic mechanical equilibrium condition of the system. It has been published as the following preprint: