Fluctuation-dissipation theorem for the Brownian motion of a polymer in solution

We consider the Brownian motion of a polymer of arbitrary shape immersed in an incompressible fluid. The polymer is represented as a permeable object which interacts with the fluid in a way described by the Debye-Bueche-Brinkman equations. We apply the ideas of non-equilibrium thermodynamics to the system of fluid plus polymer to derive the random forces which drive the fluctuations together with their fluctuation spectra. The random forces can be represented by the Landau-Lifshitz random stress tensor plus an independent random force density associated with the polymer structure. The fluid variables can be eliminated from the description to obtain a generalized Langevin equation with memory character describing translational and rotational motion of the polymer alone. Using the fluctuation spectra of the underlying random forces together with a Green's function identity for the Debye-Bueche-Brinkman equations we derive the fluctuation-dissipation theorem for the generalized Langevin equation.