  We show that thermodynamic scaling can be derived by combining the Murnaghan
equation of state (EOS) with the generalized entropy theory (GET) of glass
formation. In our theory, thermodynamic scaling arises in the non-Arrhenius
relaxation regime as a scaling property of the fluid configurational entropy
density $s_c$, normalized by its value $s_c^*$ at the onset temperature $T_A$
of glass formation, $s_c / s_c^*$, so that a constant value of $TV^{\gamma}$
corresponds to a \textit{reduced isoentropic} fluid condition. Molecular
dynamics simulations on a coarse-grained polymer melt are utilized to confirm
that the predicted thermodynamic scaling of $\tau_{\alpha}$ by the GET holds
both above and below $T_A$ and to test whether the extent $L$ of stringlike
collective motion, normalized its value $L_A$ at $T_A$, also obeys
thermodynamic scaling, as required for consistency with thermodynamic scaling.
While the predicted thermodynamic scaling of both $\tau_{\alpha}$ and $L/ L_A$
is confirmed by simulation, we find that the isothermal compressibility
$\kappa_T$ and the long wavelength limit $S(0)$ of the static structure factor
do not exhibit thermodynamic scaling, an observation that would appear to
eliminate some proposed models of glass formation emphasizing fluid `structure'
over configurational entropy. It is found, however, that by defining a low
temperature hyperuniform reference state, we may define a compressibility
relative to this condition, $\delta \kappa_T$, a transformed dimensionless
variable that exhibits thermodynamic scaling and which can be directly related
to $s_c / s_c^*$. Further, the Murnaghan EOS allows us to interpret $\gamma$ as
a measure of intrinsic anharmonicity of intermolecular interactions that may be
directly determined from the pressure derivative of the material bulk modulus.
