Non-reciprocal anti-aligning active mixtures: deriving the exact Boltzmann collision operator
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914071058579456 |
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| author | Mihatsch, Jakob Ihle, Thomas |
| author_facet | Mihatsch, Jakob Ihle, Thomas |
| contents | We consider the effect of non-reciprocity in a binary mixture of self-propelled particles with anti-aligning interactions, where a particle of type A reacts differently to a particle of type B than vice versa. Starting from a well-known microscopic Langevin-model for the particles, setting up the corresponding exact N-particle Fokker-Planck equation and making Boltzmann's assumptions of low density and one-sided molecular chaos, the non-linear active Boltzmann equation with the exact collision operator is derived. In this derivation, the effect of phase-space compression and the build-up of pair-correlations during binary interactions is explicitly taken into account, leading to a theoretical description beyond mean-field. This extends previous results for reciprocal interactions, where it was found that orientational order can emerge in a system with purely anti-aligning interactions. Although the equations of motion are more complex than in the reciprocal system, the theory still leads to analytical expressions and predictions. Comparisons with agent-based simulations show excellent quantitative agreement of the dynamic and static behavior in the low density and/or small coupling limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00357 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-reciprocal anti-aligning active mixtures: deriving the exact Boltzmann collision operator Mihatsch, Jakob Ihle, Thomas Statistical Mechanics Soft Condensed Matter We consider the effect of non-reciprocity in a binary mixture of self-propelled particles with anti-aligning interactions, where a particle of type A reacts differently to a particle of type B than vice versa. Starting from a well-known microscopic Langevin-model for the particles, setting up the corresponding exact N-particle Fokker-Planck equation and making Boltzmann's assumptions of low density and one-sided molecular chaos, the non-linear active Boltzmann equation with the exact collision operator is derived. In this derivation, the effect of phase-space compression and the build-up of pair-correlations during binary interactions is explicitly taken into account, leading to a theoretical description beyond mean-field. This extends previous results for reciprocal interactions, where it was found that orientational order can emerge in a system with purely anti-aligning interactions. Although the equations of motion are more complex than in the reciprocal system, the theory still leads to analytical expressions and predictions. Comparisons with agent-based simulations show excellent quantitative agreement of the dynamic and static behavior in the low density and/or small coupling limit. |
| title | Non-reciprocal anti-aligning active mixtures: deriving the exact Boltzmann collision operator |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2505.00357 |