Generalized Elastic Model: Fractional Langevin Description, Fluctuation Relation, and Linear Response

TL;DR

This paper develops a fractional Langevin framework for the Generalized Elastic Model, revealing how localized perturbations propagate and relating fluctuation-response relations to Fox H-functions, applicable to diverse physical systems.

Contribution

It introduces Fox H-functions as a tool to analyze the scaling properties and fluctuation relations in the Generalized Elastic Model with fractional Langevin dynamics.

Findings

Propagation of perturbations through the system is characterized.

Generalized Kubo fluctuation relations are expressed via H-functions.

The formalism applies to systems like polymers and single-file systems.

Abstract

The Generalized Elastic Model is a linear stochastic model which accounts for the behaviour of many physical systems in nature, ranging from polymeric chains to single-file systems. If an external perturbation is exerted \emph{only} on a single point $\vec{x}^\star$ (\emph{tagged probe}), it propagates throughout the entire system. Within the fractional Langevin equation framework, we study the effect of such a perturbation, in cases of a constant force applied. We report most of the results arising from our previous analysis and, in the present work, we show that the Fox $H$-functions formalism provides a compact, elegant and useful tool for the study of the scaling properties of any observable. In particular we show how the generalized Kubo fluctuation relations can be expressed in terms of $H$-functions.