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

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.

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