When does an active bath behave as an equilibrium one?

TL;DR

This paper investigates how inertial effects influence active baths, revealing that mass can restore equilibrium-like behavior by normalizing velocity distributions and recovering the Einstein relation.

Contribution

It demonstrates that inertia causes active baths to behave more like equilibrium systems, with normal velocity distributions and restored Einstein relations, contrasting with over-damped dynamics.

Findings

Inertial effects lead to Gaussian velocity distributions.

Kinetic temperature and diffusion scale as v_0^α with 1<α<2.

Inertia causes the Einstein relation to be asymptotically recovered.

Abstract

Active baths are characterized by a non-Gaussian velocity distribution and a quadratic dependence with active velocity $v_0$ of the kinetic temperature and diffusion coefficient. While these results hold in over-damped active systems, inertial effects lead to normal velocity distributions, with kinetic temperature and diffusion coefficient increasing as $\sim v_0^\alpha$ with $1<\alpha<2$. Remarkably, the late-time diffusivity and mobility decrease with mass. Moreover, we show that the equilibrium Einstein relation is asymptotically recovered with inertia. In summary, the inertial mass restores an equilibrium-like behavior.