Nonequilibrium Statistical Mechanics of Self-propelled Hard Rods

TL;DR

This paper develops a nonequilibrium statistical mechanics framework for self-propelled hard rods, deriving a modified Smoluchowski equation that captures the effects of self-propulsion and excluded volume in two dimensions.

Contribution

It introduces a new theoretical model and derivation of a modified Smoluchowski equation for self-propelled rods, incorporating nonequilibrium effects and interactions.

Findings

Derived a modified Smoluchowski equation for self-propelled rods.

Provided a dynamical derivation of Onsager's mean field excluded volume interaction.

Enhanced understanding of the interplay between self-propulsion and excluded volume effects.

Abstract

Using tools of nonequilibirum mechanics, we study a model of self-propelled hard rods on a substrate in two dimensions to quantify the interplay of self-propulsion and excluded-volume effects. We derive of a Smoluchowski equation for the configurational probability density of self-propelled rods that contains several modifications as compared to the familiar Smoluchowski equation for thermal rods. As a side-product of our work, we also present a purely dynamical derivation of the Onsager form of the mean field excluded volume interaction among thermal hard rods.