In this appendix we shall derive the Smoluchowski equation , starting from the Langevin equation (4.27), (4.28).

Using exactly the same method as in appendix A, but now applied to
we arrive at

(4.75) |

Using

= | 1 | (4.76) | |

= | (4.77) | ||

= | (4.78) |

which follow from Eqs. (4.27) and (4.28), and following the same strategy as in appendix A we arrive at

(4.79) |

It is not difficult to show that the last two terms together yield , which proves the equivalence of Eqs. (4.27), (4.28) and Eqs. (4.32), (4.33).