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 = µkBT 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.

Effective dynamics and fluctuations of a trapped probe moving in a fluid of active hard discs (a)

“…While the slow timescale should be related to diffusion, the origin of the fast timescale is the interactions between probe and bath particles since the non-interacting bath particles show the same two-step decay. Our data is not compatible with the power-law decay predicted in [45], but note that the accessible time range is restricted to a few τ r 's and we do not make any statement about the late-time decay of the force correlations. For large speeds, the fast relaxation effectively vanishes.…”

“…Solon and Horowitz have studied the relationship between diffusion coefficient and mobility of a probe moving in a bath modeled as active Brownian particles [45]. They have compared a passive fluid and an active fluid with constant (relatively small) propulsion speed of the active particles and varied the size ratio.…”

Investigation of diffusivity in nanometer‐thick yttria‐stabilized zirconia by chronoamperometry and its formalism

“…For diffusivity, the concept is analogous to mobility in semiconductors. The Einstein relation 58 defines the relationship between mobility μ and diffusivity D of electrons by: $$$$\begin{equation}\mu \ = \frac{q}{{kT}}\ D,\end{equation}$$$$…”

“…For diffusivity, the concept is analogous to mobility in semiconductors. The Einstein relation 58 defines the relationship between mobility 𝜇 and diffusivity 𝐷 of electrons by:…”

Trapped tracer in a non-equilibrium bath: dynamics and energetics

“…33,47,86 Recently, a few theoretical and simulation-based studies considered the fluctuating motion of a passive tracer in an active medium by modelling the bath particles as AOUPs. 62,[87][88][89][90] For example, the authors of ref. 89 modelled a Stirling-like heat engine in a viscoelastic active bath by considering the system as a large passive tracer interacting with the AOUPs via harmonic potentials.…”