Fick's law and Fokker-Planck Equation in inhomogeneous environments

Details Fick's law and Fokker-Planck Equation in inhomogeneous environments Fick's law and Fokker-Planck Equation in inhomogeneous environments

2007-11-06

arxiv.org/abs/0711.0847v3

Physics Letters A 372 (2008) 3941-3945

Physics

Plasma Physics

V2: English amended. V3: final version accepted by Physics Letters A

Scientific paper

10.1016/j.physleta.2008.03.014

In inhomogeneous environments, the correct expression of the diffusive flux is often not given by the Fick's law $\Gamma = - D \nabla n $. The most general hydrodynamic equation modelling diffusion is indeed the Fokker-Planck Equation (FPE). The microscopic dynamics of each specific system may affect the form of the FPE, either establishing connections between the diffusion and the convection term, as well as providing supplementary terms. In particular, the Fick's form for the Diffusion Equation may arise only in consequence of a specific kind of microscopic dynamics. It is also shown how, in the presence of sharp inhomogeneities, even the hydrodynamic FPE limit may becomes inaccurate and mask some features of the true solution, as computed from the Master Equation.

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