On some classes of open two-species exclusion processes (Q2906832)

A central issue in statistical mechanics are the properties of open systems kept in a nonequilibrium stationary state (NESS). In these systems, the key point are the fluxes of locally conserved quantities, such as the number of particles transported by the system. The only nontrivial systems for which the NESS is known explicitly are one dimensional lattice systems with stochastic dynamics. But this case is rather exceptional in that the NESS is fully described by a product measure and thus does not exhibit the long range correlations expected to be generic for NESS of realistic systems.NEWLINENEWLINEIn this paper, The authors investigate the particle fluxes and densities in the NESS of the open two-species totally asymmetric simple exclusion process (2-TASEP). This system is on a finite one-dimensional lattice of \(L\) sites: each site is either empty (referred to as hole) or occupied by a type 1 or a type 2 particle. The internal dynamics are those in which a type 1 particle can exchange with a hole or type 2 particle to its right and a type 2 particle with a hole to its right or a type 1 particle to its left.NEWLINENEWLINEThe one-dimensional 2-TASEP dynamics have been studied earlier, primarily using the so-called matrix ansatz. In the literature, there is an extended review: (i) on exchange equal rates (for the closed system on a ring and for the system on the infinite lattice); (ii) on unequal rates for the system on the ring.NEWLINENEWLINEThis paper is divided into four sections. In Section 2, the authors discuss results obtained from projecting the two-species TASEP onto a one-species TASEP (colouring). Section 3 shows a presentation of coupling arguments used to obtain some information on how the currents of the different species depend on the boundary rates. Section 4 shows cases in which the system is solvable by a matrix ansatz.