The validity of the Smoluchowski equation in the molecular theory of monatomic liquids

Publisher Website
Google Scholar
Abstract
The Smoluchowski equation for a pair of molecules (which describes the evolution of the configurational distribution function) is derived from the Liouville equation by means of a suitably formulated statement of the hypothesis of molecular chaos. This statement is based on a small-step model of the diffusion processes. No appeal is made to the Brownian motion assumption that the average momentum of a molecule obeys a linear regression law (or to the Fokker-Planck equation). Support is thereby obtained for the assertion that the success of the Kirkwood-Eisenschitz theories is due to the validity of the Smoluchowski equation independently of the validity of the Fokker-Planck equation. The nature of corrections to the Smoluchowski equation is briefly discussed.