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The advent of short-pulse lasers, nanotechnology, as well as shock-wavetechniques have created new states of matter (e.g., warm dense matter) thatcall for new theoretical tools. Ion correlations, electron correlations as wellas bound states, continuum states, partial degeneracies and quasi-equilibriumsystems need to be addressed. Bogoliubov's ideas of timescales can be used todiscuss the quasi-thermodynamics of non-equilibrium systems. A rigorousapproach to the associated many-body problem turns out to be the computation ofthe underlying pair-distribution functions g_ee, g_ei and g_ii, that directlyyield non-local exchange-correlation potentials, free energies etc., validwithin the timescales of each evolving system. An accurate classical map of thestrongly-quantum uniform electron-gas problem given by Dharma-wardana andPerrot is reviewed. This replaces the quantum electrons at T=0 by an equivalentclassical fluid at a finite temperature T_q, and having the same correlationenergy. It has been shown, but not proven, that the classical fluid g_ij areexcellent approximations to the quantum g_ij. The classical map is used withclassical molecular dynamics (CMMD) or hyper-netted-chain integral equations(CHNC) to determine the pair-distribution functions (PDFs), and hence theirthermodynamic and linear transport properties. The CHNC is very efficient forcalculating the PDFs of uniform systems, while CMMD is more adapted tonon-uniform systems. Applications to 2D and 3D quantum fluids, Simetal-oxide-field-effect transistors, Al plasmas, shock-compressed deuterium,two-temperature plasmas, pseudopotentials, as well as calculations forparabolic quantum dots are reviewed.

The Classical-Map Hyper-Netted-Chain (CHNC) method and associated novel density-functional methods for Warm Dense Matter