Microscopic theory of soft run-and-tumble particles

TL;DR

This paper develops a microscopic theory for soft run-and-tumble particles, revealing how effective attractions emerge from purely repulsive interactions at high self-propulsion, and calculates key stationary state properties.

Contribution

It provides an exact microscopic derivation and systematic perturbative calculation of effective interactions and stationary state observables for soft run-and-tumble particles.

Findings

Effective attraction arises at strong repulsion and high self-propulsion.

Systematic calculation of effective interaction vertices including loop corrections.

Quantitative characterization of stationary state properties like correlation functions and entropy production.

Abstract

Soft, repulsive run-and-tumble particles display emergent effective interactions as they appear to stick to each other in spite of the absence of attractive forces. This effective attraction emerges at strong enough repulsion and large self-propulsion. Complementing a companion paper that characterises effective attraction between two soft run-and-tumble particles [Garcia-Millan et al., Effective attraction by repulsion (2026)], here we provide a thorough derivation of our microscopic theory, which is an exact representation of the particle dynamics. We report the systematic calculation of the effective interaction vertices iteratively, in a perturbation expansion about the interaction couplings, by adding, order by order, loop corrections. We use the effective interaction vertices to calculate the two-point correlation function, fully characterising the stationary state. Other observables, such as the structure factor, overlap probability and entropy production rate are calculated as well.