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, $110\to101$ at rate $\alpha$ (leader advancement) and $101\to011$ at rate $\beta$ (follower recovery). We prove that the stationary measure on the dynamically active sector is the Gibbs measure $\pi\propto q^{H(\eta)}$, where $q=\beta/\alpha$ and $H(\eta)$ 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 $\rho\mapsto1-\rho$, with its maximum occurring at densities strictly larger than $1/2$, in contrast to the symmetric current $\rho(1-\rho)$ 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 $J\to\alpha\rho$, 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.