Brownian motion and fluctuating hydrodynamics II; A fluctuation-dissipation theorem for the slip coefficient

The Langevin equations for the linear and angular velocities of a non-spherical Brownian particle are derived from the equations governing fluctuating hydrodynamics. Arbitrary slip boundary conditions are used at the surface of the particle. It is shown that it is essential to include a random frictional force at the particle-fluid interface in order to derive the usual fluctuation-dissipation theorems for the random force and random torque on the particle. A fluctuation-dissipation theorem for the slip coefficient is given.