Kinetic Theory – Fokker-Planck Equation
In this chapter we consider a model system (protein) interacting with a surrounding medium which is only taken implicitly into account. We are interested in the dynamics on a time scale slower than the medium fluctuations. The interaction with the medium is described approximately as the sum of an average force and a stochastic force. We discuss the stochastic differential equation for 1-dimensional Brownian motion and derive the corresponding Fokker-Planck equation. We consider motion of a particle under the influence of an external force and derive the Klein-Kramers equation for diffusion in an external potential and the Smoluchowski equation as its large-friction limit. Finally we discuss the connection to the general Master equation for the probability density.