On the calculation of the self-diffusion coefficient of interacting Brownian particles

We consider two ways to calculate the self-diffusion coefficient of interacting Brownian particles. The first approach is based on the calculation of the mean square displacement of a Brownian particle starting from the Smoluchowski equation. In the second approach the self-diffusion coefficient is obtained as the product of the thermodynamic driving force and the mobility. The advantages and limitations of the two methods are discussed