Stochastic model for the dynamics of interacting Brownian particles

Using the scheme of mesoscopic non-equilibrium thermodynamics, we construct the one- and two-particle Fokker–Planck equations for a system of interacting Brownian particles. By means of these equations we derive the corresponding balance equations. We obtain expressions for the heat flux and the pressure tensor which enable one to describe the kinetic and potential energy interchange of the particles with the heat bath. Through the momentum balance, we analyze in particular the diffusion regime to obtain the collective diffusion coefficient in terms of the hydrodynamic and the effective forces acting on the Brownian particles.