Velocity Fluctuations of a Body in a Fluid

An extension of the usual treatment of Brownian motion is given. The motion of a body in a fluid is considered to be described by a quite general form of retarding force. To describe the expected fluctuations, correlation functions are obtained from a fluctuation-dissipation theorem. Under very modest conditions on the retarding force the “equipartition theorem” is obtained. Frequently, such correlation functions are obtained by postulating certain fluctuating forces. Here, no such assumption is made. However, it is possible to exhibit those fluctuating forces which would give our correlation functions. Some examples are discussed. Finally, the results for a realistic retarding force are obtained.