Abstract
An active bath, made of self-propelling units, is a nonequilibrium medium in which the Einstein relation D = μk B T between the mobility μ 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.
Highlights
Multiple methods have been developed to understand the effect of the active bath, for example using modern developments in nonequilibrium linear response theory for weakly interacting tracers [23, 24, 25] or by a perturbative analysis of the stochastic equations of motion for soft tracers [26, 27, 28]
To highlight similarities and differences, we first consider a bath of passive Brownian particles for which the Einstein relation D = μkBT between the mobility μ and diffusion coefficient D of the tracer directly follows from the Boltzmann distribution
To a good approximation that becomes exact for large tracers, the damping and noise due to the active bath obey an Einstein-like relation involving the active temperature
Summary
We consider a tracer with position and velocity (R, V) in a bath of either passive Brownian particles (PBPs) or active Brownian particles (ABPs). The ensemble is itself in a surrounding fluid at temperature T that induces a friction of coefficient γT and γB on the tracer and bath particles respectively. Among themselves, bath particles interact via a truncated harmonic potential, fi = −∇riV with V =. This allows us to vary the bath transport properties by tuning the interaction strength k while we keep the number density ρ0 = 1 fixed. We choose the interaction radius of a bath particle σB = 1, thereby fixing the length unit and work in energy units such that kB = 1.
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