  We introduce a new approach to density functional theory based on kinetic
theory, showing that the Kohn-Sham equations can be derived as a macroscopic
limit of a suitable Boltzmann kinetic equation in the limit of small mean free
path versus the typical scale of density gradients (Chapman-Enskog expansion).
To derive the approach, we first write the Schr\"odinger equation as a special
case of a Boltzmann equation for a gas of quasi-particles, with the potential
playing the role of an external source that generates and destroys particles,
so as to drive the system towards the ground state. The ions are treated as
classical particles, using the Born-Oppenheimer dynamics, or by imposing
concurrent evolution with the electronic orbitals. In order to provide
quantitative support to our approach, we implement a discrete (lattice) model
and compute, the exchange and correlation energies of simple atoms, and the
geometrical configuration of the methane molecule. Excellent agreement with
values in the literature is found.
