The induced friction on a probe moving in a nonequilibrium medium

Ji-Hui Pei, Christian Maes

Published 2024-07-13Version 1

Using a powerful combination of projection-operator method and path-space response theory, we derive the fluctuation dynamics of a slow inertial probe coupled to a steady nonequilibrium medium under the assumption of time-scale separation. The nonequilibrium can be realized by external nongradient driving on the medium particles or by their (athermal) active self-propulsion. The resulting friction on the probe is explicit as a time-correlation for medium observables and is decomposed into two terms, one entropic and proportional to the noise amplitude as in the Einstein relation for equilibrium media, and a frenetic term that can take both signs. As illustration, we give the exact expressions for the friction and noise of a probe in a rotating run-and-tumble medium and in a sheared overdamped medium. In both examples, we find an interesting transition to absolute negative probe friction as the nonequilibrium medium exhibits sufficient and persistent rotational current.