From Langevin to generalized Langevin equations for the nonequilibrium Rouse model

TL;DR

This paper derives a generalized Langevin equation for a monomer in a driven polymer chain, revealing how nonequilibrium forces influence effective dynamics through memory and noise kernels.

Contribution

It introduces a method to obtain effective nonequilibrium dynamics for a monomer in a driven Rouse model, extending Langevin equations to include memory effects.

Findings

Derived explicit memory and noise kernels for the effective dynamics.

Showed how nonequilibrium driving modifies the effective forces.

Provided insights into the inheritance of nonequilibrium properties in coarse-grained models.

Abstract

We investigate the nature of the effective dynamics and statistical forces obtained after integrating out nonequilibrium degrees of freedom. To be explicit, we consider the Rouse model for the conformational dynamics of an ideal polymer chain subject to steady driving. We compute the effective dynamics for one of the many monomers by integrating out the rest of the chain. The result is a generalized Langevin dynamics for which we give the memory and noise kernels and the effective force, and we discuss the inherited nonequilibrium aspects.