Time reversal of the overdamped Langevin equation and Fixman’s law

We show that the first order Langevin equation for the overdamped dynamics of an interacting system has a natural time reversal of simple but surprising form. This leads to a clear derivation of Fixman’s relation for how interactions modify the time dependent response of the system, and we show the application to the time dependent diffusion of dilute polymer coils. We find the generalized “Fixman Law” for dissipation with a memory kernel, and we also discuss the case of the second order Langevin Equation