On the Einstein relation between mobility and diffusion coefficient in an active bath

Abstract

An active bath, made of self-propelling units, is a nonequilibrium medium in which the Einstein relation $D=\mu k_{B}T$ between the mobility $\mu$ and the diffusivity $D$ of a tracer particle cannot be expected to hold a priori. We consider here heavy tracers for which these coefficients can be related to correlation functions which we estimate. We show that, to a good approximation, an Einstein relation does hold in an active bath upon using a different temperature which is defined mechanically, through the pressure exerted on the tracer.

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• When does an active bath behave as an equilibrium one?
• The induced friction on a probe moving in a nonequilibrium medium
• Tracer dynamics in an interacting active bath: fluctuations and energy partition
• Harmonic chain driven by active Rubin bath: transport properties and steady-state correlations
• A Cold Tracer in a Hot Bath: In and Out of Equilibrium
• Probing the limits of effective temperature consistency in actively driven systems
• Statistical mechanics of a cold tracer in a hot bath
• Negative drag force on beating flagellar-shaped bodies in active fluids
• Effective diffusion of a tracer in active bath: a path-integral approach