The induced friction on a probe moving in a nonequilibrium medium

TL;DR

This paper derives the fluctuation dynamics of a probe in a nonequilibrium medium, revealing how nonequilibrium conditions can induce negative friction and acceleration, with exact results for a rotating run-and-tumble medium.

Contribution

It introduces a new theoretical framework combining projection-operator and response theory to analyze probe friction in nonequilibrium media, including explicit formulas and phase transition insights.

Findings

Identification of entropic and frenetic contributions to friction.

Discovery of negative friction leading to probe acceleration.

Exact expressions for friction and noise in a rotating run-and-tumble medium.

Abstract

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 is realized by external nongradient driving on the medium particles or by their (athermal) active self-propulsion. The resulting friction on the probe is an explicit time-correlation for medium observables and is decomposed into two terms, one entropic, proportional to the noise variance as in the Einstein relation for equilibrium media, and a frenetic term that can take both signs. As an illustration, we give the exact expressions for the linear friction coefficient and noise amplitude of a probe in a rotating run-and-tumble medium. We find a transition to absolute negative probe friction as the nonequilibrium medium exhibits sufficient and persistent rotational current. There, the run-away of the probe to high speeds realizes a nonequilibrium-induced acceleration. Simulations show that its speed finally saturates, yielding a symmetric stationary probe-momentum distribution with two peaks.