Langevin analogy between particle trajectories and polymer configurations

TL;DR

This paper introduces a static GLE-like model for polymer configurations inspired by the Langevin analogy with particle trajectories, highlighting differences in fluctuation-response relations between static and dynamic cases.

Contribution

It proposes a static GLE-like framework satisfying the fluctuation-response relation for polymers, extending the Langevin analogy to static configurations and exploring related stochastic energetics.

Findings

Static GLE-like description generates polymer configurations.

Qualitative differences in fluctuation-response relations between static and dynamic GLEs.

Insights into stochastic energetics and fluctuation theorems for polymers.

Abstract

A diffusive trajectory drawn by the generalized Langevin equation (GLE) for a colloidal particle evokes a random fractal of a static polymer configuration. This article proposes a static GLE-like description that enables the generation of a single configuration of a polymer chain with the noise formulated to satisfy the static fluctuation-response relation (FRR) along a one-dimensional chain structure but not along a temporal coordinate. A remarkable point is qualitative differences and similarities in the FRR formulation between the static and the dynamical GLEs. Guided by the static FRR, we further make analogous arguments in the light of stochastic energetics and the steady-state fluctuation theorem.