Emergent memory from tapping collisions in active granular matter

In an equilibrium thermal environment, random elastic collisions between background particles and a tracer establish the picture of Brownian motion fulfilling the celebrated Einstein relation between diffusivity and mobility. However, extensions of the Einstein relation to link dissipation, fluctuations, and nonequilibrium dynamical mechanisms in active matter systems are still debated. Here, we investigate experimentally the impact of an active background on a passive tracer using vibrationally excited active particles, that result in multiple correlated tapping collisions with the tracer, for which a persistent memory emerges in the dynamics. The system is described by a generalized active Einstein relation that constrains fluctuations, dissipation, and effective activity, by taking the emerging tracer memory into account. Since the resulting persistence can largely be tuned by the environmental density and motility, our findings can be useful to engineer properties of various active systems in biomedical applications, microfluidics, chemical engineering, or swarm robotics.Einstein relations in non-equilibrium active matter systems break upon increase of fluctuations and changes in the system's dissipative properties. By observing the tapping collisions of a tracer in a bath of vibrationally excited active granular particles, the authors propose a generalized active Einstein relation accounting for memory effects.