text: * In non-homogeneous media, the diffusion coefficient varies in space, . This dependence does not affect Fick's first law but the second law changes: 
  * In anisotropic media, the diffusion coefficient depends on the direction. It is a symmetric tensor . Fick's first law changes to  it is the product of a tensor and a vector:  For the diffusion equation this formula gives  The symmetric matrix of diffusion coefficients  should be positive definite. It is needed to make the right hand side operator elliptic.
  * For inhomogeneous anisotropic media these two forms of the diffusion equation should be combined in 
  * The approach based on Einsteins mobility and Teorell formula gives the following generalization of Ficks equation for the multicomponent diffusion of the perfect components:  where  are concentrations of the components and  is the matrix of coefficients. Here, indices  and  are related to the various components and not to the space coordinates.
  The Chapman–Enskog formulae for diffusion in gases include exactly the same terms. These physical models of diffusion are different from the test models  which are valid for very small deviations from the uniform equilibrium. Earlier, such terms were introduced in the Maxwell–Stefan diffusion equation.
  For anisotropic multicomponent diffusion coefficients one needs a rank-four tensor, for example , where  refer to the components and  correspond to the space coordinates.