The Lennard-Jones Lecture. The concept of Brownian motion in modern statistical mechanics

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Abstract
The statistical-mechanical bases for the fundamental equations describing Brownian motion are presented. These equations are the Langevin, Fokker–Planck and Smoluchowski equations. The conditions under which they are valid for single and many Brownian particle systems are delineated. The imposition of boundary conditions on these equations is discussed. The application of these results to reaction kinetics, diffusion-limited aggregation and cluster–cluster aggregation is briefly described.