Symmetry properties of the large-deviation function of the velocity of a self-propelled polar particle

TL;DR

This study investigates the large deviation function of a self-propelled polar granular particle's velocity, revealing non-Gaussian behavior, a kink at zero velocity, and a linear antisymmetric part akin to fluctuation relations, with implications for understanding active matter dynamics.

Contribution

It uncovers the symmetry properties of the large deviation function of velocity in a self-propelled granular particle, highlighting a fluctuation relation-like behavior in a non-Gaussian context.

Findings

Large deviation function is strongly non-Gaussian with a kink at zero velocity.

Antisymmetric part of the LDF is linear, resembling fluctuation relations.

An analogue of phase space contraction rate matches independent estimates.

Abstract

A geometrically polar granular rod confined in 2-D geometry, subjected to a sinusoidal vertical oscillation, undergoes noisy self-propulsion in a direction determined by its polarity. When surrounded by a medium of crystalline spherical beads, it displays substantial negative fluctuations in its velocity. We find that the large deviation function (LDF) for the normalized velocity is strongly non-Gaussian with a kink at zero velocity, and that the antisymmetric part of the LDF is linear, resembling the fluctuation relation known for entropy production, even when the velocity distribution is clearly non-Gaussian. We extract an analogue of the phase space contraction rate and find that it compares well with an independent estimate based on the persistence of forward and reverse velocities.