Hydrodynamic Limit of the Inhomogeneous $\ell$-TASEP with Open Boundaries: Derivation and Solution

Dan D. Erdmann-Pham, Khanh Dao Duc, Yun S. Song

Published 2018-03-15Version 1

The totally asymmetric simple exclusion process, which describes the transport of interacting particles in a lattice, has been actively studied over the past several decades. For general cases where particles have an extended size and hop at site-dependent rates, however, theoretically analyzing the dynamics has remained elusive. Here, we present such an analysis by deriving and solving the hydrodynamic limit. We obtain closed-form formulas for steady-state particle densities and currents, as well as phase transition boundaries. Surprisingly the latter depend on only four parameters: the particle size and the first, the last, and the minimum hopping rates. Our results agree well with Monte Carlo simulations and can be used in inference.