Abstract
The Brownian forces for a Hookean dumbbell model with internal viscosity are characterized using the fluctuation-dissipation theorem and assuming that the momentum and configuration of the chain fluctuate on separate time scales. A Langevin-type approach in the full phase-space of the dumbbell is used to derive the proper stochastic differential equation. By considering both the stochastic differential equation, or equation of motion, and the equivalent Fokker-Planck equation, or diffusion equation, a contraction is made to the configuration space of the dumbbell. The resulting diffusion equation is compared to the models of previous works employing internal viscosity. It is found that some previous models do indeed satisfy the fluctuation-dissipation theorem (Kuhn and Kuhn, Booij and van Wiechen), whereas others do not.
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