Activity-driven clustering and many-body steady state of jamming run-and-tumble particles

Fuente: arXiv
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Autores principales: Hahn, Leo, Guillin, Arnaud, Michel, Manon
Formato: Preprint
Publicado: 2025
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author Hahn, Leo
Guillin, Arnaud
Michel, Manon
author_facet Hahn, Leo
Guillin, Arnaud
Michel, Manon
contents We exactly resolve the three-particle steady state of run-and-tumble particles with jamming interactions, providing the first microscopic description beyond two bodies. The invariant measure, derived via a piecewise-deterministic Markov process description and symmetry principles, reveals persistent, separated, and diffusive regimes ruled by the activity parameter. A geometric cascade of scales in the activity parameter organizes the structural weights, showing the separated phase dominates at finite activity, while non-uniformity plays only a minor role. Extending these results to larger systems, we show that the $N$-body steady state inherits the same organization: the number of clusters becomes sharply defined by the activity value, with crossover boundaries whose slopes diverge with $N$. We also show how the activity plays a role similar to a fugacity conjugate to cluster number, yielding a grand-canonical-like structure emerging directly from the microscopic dynamics. This framework lays the groundwork for a systematic microscopic theory of active many-body steady states.
format Preprint
id arxiv_https___arxiv_org_abs_2509_08945
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Activity-driven clustering and many-body steady state of jamming run-and-tumble particles
Hahn, Leo
Guillin, Arnaud
Michel, Manon
Statistical Mechanics
Probability
We exactly resolve the three-particle steady state of run-and-tumble particles with jamming interactions, providing the first microscopic description beyond two bodies. The invariant measure, derived via a piecewise-deterministic Markov process description and symmetry principles, reveals persistent, separated, and diffusive regimes ruled by the activity parameter. A geometric cascade of scales in the activity parameter organizes the structural weights, showing the separated phase dominates at finite activity, while non-uniformity plays only a minor role. Extending these results to larger systems, we show that the $N$-body steady state inherits the same organization: the number of clusters becomes sharply defined by the activity value, with crossover boundaries whose slopes diverge with $N$. We also show how the activity plays a role similar to a fugacity conjugate to cluster number, yielding a grand-canonical-like structure emerging directly from the microscopic dynamics. This framework lays the groundwork for a systematic microscopic theory of active many-body steady states.
title Activity-driven clustering and many-body steady state of jamming run-and-tumble particles
topic Statistical Mechanics
Probability
url https://arxiv.org/abs/2509.08945