  The classical map hypernetted-chain (CHNC) method for interacting electrons
uses a kinetic energy functional in the form of a classical-fluid temperature.
Here we show that the CHNC generated two-body densities and pair-distribution
functions (PDFs) correspond to $N$-representable densities. Comparisons of
results from CHNC with quantum Monte Carlo (QMC) and Path Integral Monte Carlo
(PIMC) are used to validate the CHNC results. Since the PDFs are sufficient to
obtain the equation of state or linear-response properties of electron-ion
systems, we apply the CHNC method for fully classical calculations of
electron-ion systems in the quantum regime, using hydrogen at 4000K and 350
times the solid density as an example since QMC comparisons are available. We
also present neutral pseudo-atom (NPA) calculations which use rigorous
density-functional theory (DFT) to reduces the many nuclear problem to an
effective one-ion problem. The CHNC PDFs and NPA results agree well with the
ion-ion, electron-ion and electron-electron PDFs from QMC, PIMC, or DFT coupled
to molecular dynamics simulations where available. The PDFs of a 2D
electron-hole system at 5K are given as an example of 2D `warm dense' matter
where the electrons and the counter particles (holes) are all in the quantum
regime. Basic methods like QMC, PIMC or even DFT become prohibitive while CHNC
methods, being independent of the number of particles or the temperature, prove
to be easily deployable.
