  We present an extension of the density-functional theory (DFT) formalism for
lattice gases to systems with internal degrees of freedom. In order to test
approximations commonly used in DFT approaches, we investigate the statics and
dynamics of occupation (density) profiles in the one-dimensional Potts model.
In particular, by taking the exact functional for this model we can directly
evaluate the quality of the local equilibrium approximation used in
time-dependent density-functional theory (TDFT). Excellent agreement is found
in comparison with Monte Carlo simulations. Finally, principal limitations of
TDFT are demonstrated.
