Hydrodynamic behavior of the two-TASEP

Abstract

Abstract We address the question of the hydrodynamic behavior of a two-species generalization of the TASEP, called two-TASEP, introduced by Derrida (1996 Statphys-19: 19th IUPAP Int. Conf. Statistical Physics) and Mallick (1996 J. Phys. A: Math. Gen. 29 5375). We find that the auxiliary variables, introduced previously in the literature to express the density dependence of particle currents, turn out to be the Riemann variables of the conservation equations. This allows us to work out quite explicitly the rarefaction and shock solutions and to completely solve the associated Riemann problem. Our theoretical results are confirmed by Monte Carlo simulations.