“…While this proof assumes a finite number of local configurations on each site, recent works obtained the steady-state distributions of different types of generalized zero range processes (ZRP)-stochastic hopping models on a lattice with the hopping rate depending on the occupation number-with periodic boundary conditions [6,22,21] and a single-species ZRP with open boundary conditions [4] using the matrix product ansatz with an unbounded number of configurations. Given the previous works on models with multiple species of particles [17,27,3,7,11,15,10,28,13], a naturally arising question is the following: is it possible to obtain the steady-state distribution of the two-species open 1D ZRP using the matrix product method? The two-species model is important because it is closely related to many interesting statistical physics phenomena such as the behavior of shaken granular gases in which the grains come in one of two sizes, and the behavior of networks with directed edges (see the review article [12] and references therein).…”