Correlated motion of 2 particles in a fluid

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Abstract
We derive a generalized Langevin equation for the simultaneous motion of two structureless particles (solute molecules) in a fluid. The resulting equations contain, in addition to the usual self memory integral term, a cross memory (or solvent-mediated drag) term which is a time-dependent generalization of the so-called hydrodynamic interaction. The cross memory function is expressed explicitly in terms of velocity cross correlation functions and may thus be evaluated numerically in molecular dynamics experiments.