  A common paradigm used in the construction of equations of state is to
decompose the thermodynamics into a superposition of three terms: a
static-lattice cold curve, a contribution from the thermal motion of the
nuclei, and a contribution from the thermal excitation of the electrons. While
statistical mechanical models for crystals provide tractable framework for the
nuclear contribution in the solid phase, much less is understood about the
nuclear contribution above the melt temperature ($C_v^{(\text{nuc})}\approx
3R$) and how it should transition to the high-temperature limit
($C_v^{(\text{nuc})} \sim \frac{3}{2}R$). In this work, we describe an
algorithm for extracting both the thermal nuclear and thermal electronic
contributions from quantum molecular dynamics (QMD). We then use the VASP QMD
package to probe thermal nuclear behavior of liquid aluminum at normal density
to compare the results to semi-empirical models -- the Johnson generic model,
the Chisolm high-temperature liquid model, and the CRIS model.
