  We utilize the lattice cluster theory (LCT) of polymer fluids to show that
the configurational entropy, enthalpy, and internal energy are all closely
interrelated, as suggested by recent measurements by Caruthers and Medvedev, so
that the generalized entropy theory (GET) of glass formation, a combination of
the LCT and Adam-Gibbs model, can be recast in terms of any of these
thermodynamic properties as a matter of convenience. Thermodynamic scaling, a
form of density-temperature scaling exhibited by dynamic and some thermodynamic
properties, is used to assess which thermodynamic properties are most naturally
linked to dynamics, and we explore the origin of this scaling by both direct
calculations based on the GET and molecular dynamics simulations of a
coarse-grained polymer model. Through a combination of our comprehensive
modeling of thermodynamic properties using the LCT and the highly predictive
GET model for how the fluid thermodynamics relate to its dynamics, along with
simulation results confirming these theoretical frameworks, we obtain insights
into thermodynamic aspects of collective motion and the slow $\beta$-relaxation
processes of glass-forming liquids.
