  Density functional theory (DFT) is a powerful theoretical tool widely used in
such diverse fields as computational condensed matter physics, atomic physics,
and quantum chemistry. DFT establishes that a system of $N$ interacting
electrons can be described uniquely by its single-particle density
$n(\boldsymbol{r})$, instead of the $N$-body wave function, yielding an
enormous gain in terms of computational speed and memory storage space. Here,
we use time-dependent DFT to show that a classical collisionless plasma can
always, in principle, be described by a set of fluid equations for the
single-particle density and current. The results of DFT guarantee that an exact
closure relation, fully reproducing the Vlasov dynamics, necessarily exists,
although it may be complicated (nonlocal in space and time, for instance) and
difficult to obtain in practice. This goes against the common wisdom in plasma
physics that the Vlasov and fluid descriptions are mutually incompatible, with
the latter inevitably missing some "purely kinetic" effects.
