Zwanzig 1D Reduction

In this chapter, we reviewed the main ideas of Robert Zwanzig to arrive at a more general and rigorous derivation of the Fick-Jacobs equation. The method consists of performing a reduction in the number of coordinates from the two- or three-dimensional Smoluchowski equation to a one-dimensional description. The key point of this derivation is the assumption of equilibration in the transverse direction. We also discussed the main properties of the diffusion coefficient’s transient behavior as function of time.