Summary
The Fokker-Planck equation for the distribution function of a Brownian sphere is derived from the exact hierarchy of kinetic equations for a massive sphere in a bath of smaller spheres, using a multiple-time-scale analysis. Our earlier derivation is specialized to the limiting cases where the bath is either an ideal or Boltzmann gas. The resulting simplifications allow more physical insight, and lead to explicit expressions for the friction coefficient.
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Bocquet, L., Hansen, J.P. & Piasecki, J. A kinetic model for Brownian motion. Il Nuovo Cimento D 16, 981–991 (1994). https://doi.org/10.1007/BF02458783
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DOI: https://doi.org/10.1007/BF02458783