MACROSCOPIC EQUATION-OF-MOTION IN INHOMOGENEOUS-MEDIA - A MICROSCOPICTREATMENT

The dynamical evolution of a Brownian particle in an inhomogeneous med ium with spatially varying friction and temperature field is important to understand conceptually. It requires to address the basic problem of relative Stability of states in nonequilibrium systems which has be en a subject of debate for over several decades. The theoretical treat ments adopted so far are mostly phenomenological in nature. In this wo rk we give a microscopic treatment of this problem. We derive the Lang evin equation of motion and the associated Fokker-Planck equation. The correct reduced description of the Kramers equation in the overdamped limit (Smoluchowski equation) is obtained. Our microscopic treatment may be helpful in understanding the working of thermal ratchets, a pro blem of much current interest.