NON-MARKOVIAN BROWNIAN-MOTION IN A VISCOELASTIC FLUID

A theory of non-Markovian translational Brownian motion in a Maxwell f luid is developed. A universal kinetic equation for the joint probabil ity distribution of position, velocity, and acceleration of a Brownian particle is derived directly from the extended dynamic equations for the system. Unlike the extended Fokker-Planck equation which correspon ds to Mori-Kubo generalized Langevin equation and provides only with c alculations of one-time moments, the universal kinetic equation obtain ed gives complete statistical description of the process. In particula r, an exact generalized Fokker-Planck equation in the velocity space v alid for any time instant is derived for the free non-Markovian Browni an motion. It shows that both the ''master telegraph'' and the respect ive kinetic equations, obtained in the molecular theory of Brownian mo tion, are type of approximations. The long and short time behavior of velocity and force correlations for a free Brownian particle is invest igated in the general case of a nonequilibrium initial value problem. A corresponding diffusion equation in the coordinate space, and the ge neralized Einstein relation between the diffusion coefficient and the mobility are derived. (C) 1996 American Institute of Physics.