Fluctuating motion in an active environment

TL;DR

This paper derives a generalized Langevin equation describing the fluctuating motion of a probe in an active medium, revealing non-dissipative corrections to fluctuation-dissipation relations due to activity.

Contribution

It introduces a theoretical framework for understanding probe dynamics in active environments, explicitly deriving corrections to fluctuation-dissipation relations.

Findings

Active medium alters probe inertia due to persistence effects.

Friction kernel is modified by activity.

Generalized Langevin equation captures active vs passive media differences.

Abstract

We derive the fluctuation dynamics of a probe in weak coupling with a "living" medium, modeled as particles undergoing an active Ornstein-Uhlenbeck dynamics. Nondissipative corrections to the fluctuation-dissipation relation are written out explicitly in terms of time-correlations in the active medium. A first term changes the inertial mass of the probe, as a consequence of the persistence of the active medium. A second correction modifies the friction kernel. The resulting generalized Langevin equation benchmarks the motion induced on probes immersed in active versus passive media. The derivation uses nonequilibrium response theory.