Can activity be transmitted from smaller to larger scales? We show such a transfer from a homogeneous active medium to a Newtonian spherical probe. The active medium consists of faster and dilute self-propelled particles, modeled as run-and-tumble particles in 1D or as active Brownian particles in 2D. We derive the reduced fluctuating dynamics of the probe valid for arbitrary probe velocity, characterized by a nonlinear friction and a velocity-dependent noise. There appear several distinct regimes: a standard regime where the probe exhibits passive Brownian motion, and peculiar active regimes where the probe becomes self-propelled with high persistence, and its velocity distribution begets peaks at non-zero values.
Those peaks and their persistence are quantitatively obtained and are perfectly confirmed by numerical simulations.
 In 1D, a soft coupling is necessary, whereas in 2D, more realistic interactions, such as Lennard-Jones, suffice.
Our study thus reveals how active motion can be transmitted between different scales solely via the induced friction and noise.

Joint work with Jihui Pei -  KU Leuven