  The thermodynamic approach to density functional theory (DFT) is used to
derive a versatile theoretical framework for the treatment of
finite-temperature (and in the limit, zero temperature) Bose-Einstein
condensates (BECs). The simplest application of this framework, using the
overall density of bosons alone, would yield the DFT of Nunes (1999). It is
argued that a significant improvement in accuracy may be obtained by using
additional density fields: the condensate amplitude and the anomalous density.
Thus, two advanced schemes are suggested, one corresponding to a generalized
two-fluid model of condensate systems, and another scheme which explicitly
accounts for anomalous density contributions and anomalous effective
potentials. The latter reduces to the Hartree-Fock-Bogoliubov approach in the
limit of weak interactions. For stronger interactions, a local density
approximation is suggested, but its implementation requires accurate data for
the thermodynamic properties of uniform interacting BEC systems, including
fictitious perturbed states of such systems. Provided that such data becomes
available, e.g., from quantum Monte Carlo computation, DFT can be used to
obtain high-accuracy theoretical results for the equilibrium states of BECs of
various geometries and external potentials.
