Tandem Exclusion Process

Abstract

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, $110\to 101$ at rate $\hat{I}\pm$ (leader advancement) and $101\to 011$ at rate ${\hat{I}}^2$ (follower recovery). We prove that the stationary measure on the dynamically active sector is the Gibbs measure $\ddot{I}€\propto q^{H(\hat{I}\cdot )}$, where $q={\hat{I}}^2/\hat{I}\pm$ and $H(\hat{I}\cdot )$ 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 $\ddot{I}\mapsto 1-\ddot{I}$, with its maximum occurring at densities strictly larger than $1/2$, in contrast to the symmetric current $\ddot{I}(1-\ddot{I})$ 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 $J\to \hat{I}\pm \ddot{I}$, 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.