Finite-temperature DFT has become of topical interest, partly due to the
increasing ability to create novel states of warm-correlated matter (WCM).
Subclasses of WCM are Warm-dense matter (WDM), ultra-fast matter (UFM), and
high-energy density matter (HEDM), containing electyrons (e) and ions (i).
Strong e-e, i-i and e-i correlation effects and partial degeneracies are found
in these systems where the electron temperature Te is comparable to the
electron Fermi energy. The ion subsystem may be solid, liquid or plasma, with
many states of ionization with ionic charge Zj. Quasi-equilibria with the
ion temperature Ti=Te are common. The ion subsystem in WCM can no longer
be treated as a passive "external potential", as is customary in T=0 density
functional theory (DFT) dominated by solid-state theory or quantum chemistry.
Hohenberg-Kohn-Mermin theory can be used for WCMs if finite-T
exchange-correlation (XC) functionals are available. They are functionals of
both the one-body electron density ne and the one-body ion densities
ρj. A method of approximately but accurately mapping the quantum
electrons to a classical Coulomb gas enables one to treat electron-ion systems
entirely classically at any temperature and arbitrary spin polarization, using
exchange-correlation effects calculated {\it in situ}, directly from the
pair-distribution functions. This eliminates the need for any XC-functionals,
or the use of a Born-Oppenheimer approximation. This classical map has been
used to calculate the equation of state of WDM systems, and construct a
finite-T XC functional that is found to be in close agreement with recent
quantum path-integral simulation data. In this review current developments and
concerns in finite-T DFT, especially in the context of non-relativistic
warm-dense matter and ultra-fast matter will be presented.Comment: Presented at the DFT16 meeting in Debrecen, Hungary, September 2015,
held on the 50th anniversary of Kohn-Sham Theory, 10 pages, 3 figure