Conformation dependent damping and generalization of fluctuation-dissipation relation

TL;DR

This paper generalizes the fluctuation-dissipation relation for systems with conformation-dependent damping, deriving an equilibrium distribution that extends Boltzmann statistics to more complex, shape-dependent damping scenarios.

Contribution

It introduces a generalized fluctuation-dissipation relation for conformation-dependent damping and derives the corresponding equilibrium distribution function.

Findings

Derived a new equilibrium distribution for conformation-dependent damping

Showed convergence to Boltzmann distribution in uniform damping limit

Implications for barrier crossing processes with non-uniform damping

Abstract

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.