Duality for the multispecies stirring process with open boundaries

Abstract

We study the stirring process with N − 1 species on a generic graph G=(V,E) with reservoirs. The multispecies stirring process generalizes the symmetric exclusion process, which is recovered in the case N = 2. We prove the existence of a dual process defined on an extended graph G~=(V~,E~) which includes additional sites in V~∖V where dual particles get absorbed in the long-time limit. We thus obtain a characterization of the non-equilibrium steady state of the boundary-driven system in terms of the absorption probabilities of dual particles. The process is integrable for the case of the one-dimensional chain with two reservoirs at the boundaries and with maximally one particle per site. We compute the absorption probabilities by relying on the underlying gl(N) symmetry and the matrix product ansatz. Thus one gets a closed-formula for (long-ranged) correlations and for the non-equilibrium stationary measure. Extensions beyond this integrable set-up are also discussed.