We derive drift-diffusion systems describing transport processes starting from free energy and equilibrium solutions by a unique method. We include several statistics, heterostructures and cross diffusion. The resulting systems of nonlinear partial differential equations conserve mass and positivity, and have a Lyapunov function (free energy). Using the inverse Hessian as mobility, non-degenerate diffusivity matrices turn out to be diagonal, or -in the case of cross diffusion -even constant. (2000). 35K55, 80A20, 82D37, 82C31, 35B50, 35G25.
Mathematics Subject Classification