Tandem Exclusion Process
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913177952845824 |
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| author | Ngoc, Ngo Phuoc Nguyen Nhung, Lam Thi Thi, Huynh Anh |
| author_facet | Ngoc, Ngo Phuoc Nguyen Nhung, Lam Thi Thi, Huynh Anh |
| contents | We introduce the \emph{tandem exclusion process} (TEP), a one-dimensional stochastic lattice model motivated by tandem running in ants. Particles evolve through two cooperative local transitions, $110\to101$ at rate $α$ (leader advancement) and $101\to011$ at rate $β$ (follower recovery). We prove that the stationary measure on the dynamically active sector is the Gibbs measure $π\propto q^{H(η)}$, where $q=β/α$ and $H(η)$ counts neighboring occupied pairs, and derive exact closed-form expressions for the stationary current and spatial correlations using transfer-matrix methods. The current is asymmetric under particle--hole exchange $ρ\mapsto1-ρ$, with its maximum occurring at densities strictly larger than $1/2$, in contrast to the symmetric current $ρ(1-ρ)$ of the totally asymmetric simple exclusion process (TASEP). For $q>1$, cooperative dynamics enhances the current above the TASEP value and generates strong spatial clustering; in the limit $q\to\infty$, the current approaches $J\toαρ$, corresponding to nearly unconstrained collective transport. These results suggest that tandem coordination alone can substantially enhance collective transport efficiency at moderate and high densities, even without pheromone-mediated long-range communication. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_01568 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tandem Exclusion Process Ngoc, Ngo Phuoc Nguyen Nhung, Lam Thi Thi, Huynh Anh Statistical Mechanics We introduce the \emph{tandem exclusion process} (TEP), a one-dimensional stochastic lattice model motivated by tandem running in ants. Particles evolve through two cooperative local transitions, $110\to101$ at rate $α$ (leader advancement) and $101\to011$ at rate $β$ (follower recovery). We prove that the stationary measure on the dynamically active sector is the Gibbs measure $π\propto q^{H(η)}$, where $q=β/α$ and $H(η)$ counts neighboring occupied pairs, and derive exact closed-form expressions for the stationary current and spatial correlations using transfer-matrix methods. The current is asymmetric under particle--hole exchange $ρ\mapsto1-ρ$, with its maximum occurring at densities strictly larger than $1/2$, in contrast to the symmetric current $ρ(1-ρ)$ of the totally asymmetric simple exclusion process (TASEP). For $q>1$, cooperative dynamics enhances the current above the TASEP value and generates strong spatial clustering; in the limit $q\to\infty$, the current approaches $J\toαρ$, corresponding to nearly unconstrained collective transport. These results suggest that tandem coordination alone can substantially enhance collective transport efficiency at moderate and high densities, even without pheromone-mediated long-range communication. |
| title | Tandem Exclusion Process |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2606.01568 |