with the mobility Γ Γ and the free energy F . DDFT can be derived from the microscopic equations of motion for a colloidal system (Langevin equations or Smoluchowski equation) based on the adiabatic approximation, which corresponds to the assumption that the two-body distribution in a nonequilibrium system is identical to that in an equilibrium system with the same one-body density. For a system of noninteracting particles, DDFT reduces to the standard diffusion equation.