Nonergodic Brownian Dynamics and the Fluctuation-Dissipation Theorem

TL;DR

This paper explores nonergodic Brownian motion using the generalized Langevin equation, revealing anomalous diffusion behaviors and conditions under which the fluctuation-dissipation theorem holds, with implications for directed transport in Brownian motors.

Contribution

It introduces a framework for understanding nonergodic Brownian dynamics and identifies conditions for the fluctuation-dissipation theorem in such systems.

Findings

Nonergodic Brownian motion can exhibit ballistic or localized dynamics.

Thermal noise can enhance directed transport in Brownian motors.

Conditions for the fluctuation-dissipation theorem are specified.

Abstract

Nonergodic Brownian motion is elucidated within the framework of the generalized Langevin equation. For thermal noise yielding either a vanishing or a divergent zero-frequency friction strength, the non-Markovian Browninan dynamics exhibits a riveting, anomalous diffusion behavior being characterized by a ballistic or possibly also a localized dynamics. As a consequence, such tailored thermal noise may cause a net acceleration of directed transport in a rocking Brownian motor. Two notable conditions for the thermal noise are identified in order to guarantee the fluctuation-dissipation theorem of first kind.