Stationary superstatistics distributions of trapped run-and-tumble particles

TL;DR

This paper analyzes the stationary distributions of trapped active particles, revealing their superstatistical nature and linking nonequilibrium active motion to concepts like local equilibrium and effective temperature.

Contribution

It introduces a thermophoretic potential framework for active particles, providing new insights into their nonequilibrium stationary distributions and the emergence of novel distribution modes.

Findings

Stationary distributions are superstatistics in nature.

Persistent motion leads to non-Boltzmann-Gibbs distributions.

Coupling of motion and potential creates new distribution modes.

Abstract

We present an analysis of the stationary distributions of run-and-tumble particles trapped in external potentials in terms of a thermophoretic potential, that emerges when trapped active motion is mapped to trapped passive Brownian motion in a fictitious inhomogeneous thermal bath. We elaborate on the meaning of the non-Boltzmann-Gibbs stationary distributions that emerge as a consequence of the persistent motion of active particles. These stationary distributions are interpreted as a class of distributions in nonequilibrium statistical mechanics known as superstatistics. Our analysis provides an original insight on the link between the intrinsic nonequilibrium nature of active motion and the well-known concept of local equilibrium used in nonequilibrium statistical mechanics, and contributes to the understanding of the validity of the concept of effective temperature. Particular cases of interest, regarding specific trapping potentials used in other theoretical or experimental studies, are discussed. We point out as an unprecedented effect, the emergence of new modes of the stationary distribution as a consequence of the coupling of persistent motion in a trapping potential that varies highly enough with position.