Conformation dependent damping and generalization of fluctuation-dissipation relation

Damping on an object generally depends on its conformation (shape size etc.). We consider the Langevin dynamics of a model system with a conformation dependent damping and generalize the fluctuation dissipation relation to fit in such a situation. We derive equilibrium distribution function for such a case which converges to the standard Boltzmann form at the limit of uniform damping. The results can have implications, in general, for barrier overcoming processes where standard Boltzmann statistics is slow.