  The simplest density functional theory due to Thomas, Fermi, Dirac and
Weizsacker is employed to describe the non-equilibrium thermodynamic evolution
of an electron gas. The temperature effect is introduced via the Fermi-Dirac
entropy, while the irreversible dynamics is described by a nonlinear diffusion
equation. A dissipative Kohn-Sham equation is also proposed, which improves the
Thomas-Fermi-Weizsacker kinetic functional.
