We now concentrate on one bead, say bead no. *n*, while keeping all the
other beads fixed. Its equilibrium distribution is given by

(6.1) |

According to Eq. (4.30) and Eq. (4.27) the Langevin equation describing the motion of the bead then is, with

(6.2) |

where we have assumed that is independent on . The same reasoning may be applied to all other beads, leaving us with the equations of motion

Eq. (6.4) applies when .

Before starting to analyse these equations in the next section, let us
derive one simple result:

= | (6.7) | ||

= | (6.8) |

So , which is perfectly understandable.