Activity-driven clustering and many-body steady state of jamming run-and-tumble particles
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911394794831872 |
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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 |