Kinetic theory derivation of a pair configuration space diffusion equation

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Abstract
A repeated ring kinetic theory is derived to describe the thermal fluctuations of two test particles in a fluid. The kinetic equation incorporates the interaction of the two particles via the potential of the mean force, their uncorrelated Enskog propagation, and multiply correlated collisions among the test particles and the bath particles. By projecting on the configuration space of the test particles, an equation of the form of a diffusion equation is obtained, but with a microscopically defined diffusion tensor. The configuration and time dependent diffusion tensor is given by a time correlation function and can be evaluated for a given molecular model.