LANGEVIN EQUATION FOR THE DENSITY OF A SYSTEM OF INTERACTING LANGEVINPROCESSES

We present a simple derivation of the stochastic equation obeyed by th e density function for a system of Langevin processes interacting via a pairwise potential. The resulting equation is considerably different from the phenomenological equations usually used to describe the dyna mics of non-conserved (model A) and conserved (model B) particle syste ms. The major feature is that the spatial white noise for this system appears not additively but multiplicatively. This simply expresses the fact that the density cannot fluctuate in regions devoid of particles . The steady state for the density function may, however, still be rec overed formally as a functional integral over the coursed grained free energy of the system as in models A and B.