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In an equilibrium thermal environment, random elastic collisions betweenbackground particles and a tracer establish the picture of Brownian motionfulfilling the celebrated Einstein relation between diffusivity and mobility.In nature, environments often comprise collections of autonomously movingobjects that exhibit fascinating non-equilibrium phenomena and are nowadaystermed active matter. We investigate experimentally the impact of an activebackground on a passive tracer using vibrationally excited active particles.They produce multiple correlated tapping collisions with the tracer, for whicha persistent memory emerges in the dynamics. The system is described by ageneralized 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 environmentaldensity and motility, our findings can be useful to engineer properties ofvarious active systems in biomedical applications, microfluidics, chemicalengineering, or swarm robotics.

Emergent memory from tapping collisions in active granular matter