Statistical Mechanical Theory of Transport Processes. IX. Contribution to the Theory of Brownian Motion

Abstract

The equations of Brownian motion are derived from Liouville's equation in a treatment which parallels Kirkwood's statistical mechanical analysis but which is based upon the theory of phase space transformation functions. The transformation function obeys Liouville's equation and thus expresses the equations of motion; it is obtained as a solution of that equation by a consistent method of successive approximations which treats the forces as perturbations. Retention of first‐order terms only in this solution leads to the Chandrasekhar equation and yields a tractable relation between the friction constant and the intermolecular forces. The restrictions imposed by the present derivation on the molecular interpretation of the equations of Brownian motion are discussed.