Consider a particle suspended in a liquid. On its path through the liquid it will continuously collide with the liquid molecules. Because on average the particle will collide more often on the front side than on the back side, it will experience a systematic force proportional with its velocity, and directed opposite to its velocity. Besides this systematic force the particle will experience a stochastic force \( \mathbf{F}(t) \). The equations of motion are

• \( \frac{d\mathbf{r}}{dt}=\mathbf{v} \) and
• \( \frac{d\mathbf{v}}{dt}=-\xi \mathbf{v}+\mathbf{F} \).