Generalized Elastic Model yields Fractional Langevin Equation

TL;DR

This paper derives a fractional Langevin equation from a generalized elastic model, explaining stochastic dynamics in systems like membranes and polymers, and highlights its unique compliance with fluctuation-dissipation relations under thermal conditions.

Contribution

It introduces a novel derivation of the fractional Langevin equation from a generalized elastic model, establishing its unique relation to fluctuation-dissipation within a new family of FBM equations.

Findings

The derived FLE satisfies the fluctuation-dissipation relation for thermal initial conditions.

The FLE accurately describes the fluctuations of donor-acceptor distances in proteins.

A non-FD FLE is obtained for non-thermal initial conditions.

Abstract

Starting from a generalized elastic model which accounts for the stochastic motion of several physical systems such as membranes, (semi)flexible polymers and fluctuating interfaces among others, we derive the fractional Langevin equation (FLE) for a probe particle in such systems, in the case of thermal initial conditions. We show that this FLE is the only one fulfilling the fluctuation-dissipation (FD) relation within a new family of fractional Brownian motion (FBM) equations. The FLE for the time-dependent fluctuations of the donor-acceptor distance in a protein, is shown to be recovered. When the system starts from non-thermal conditions, the corresponding FLE, which does not fulfill FD relation, is derived.