## Duality for the multispecies stirring process with open boundaries

To construct a model for non-equilibrium statistical mechanics, the system is typically brought into contact with two thermodynamic baths, referred to as boundary reservoirs. These reservoirs impose their own density of particles at the system's boundary, generating a current. In the long-time limit, a non-equilibrium steady state sets in, characterized by a stationary value of the current. Currently, there is a growing interest for multi-component systems, i.e. models where many dierent species of particle (sometimes called colours) are present. In addition to the occupation of available spaces, interactions between dierent species become possible. Starting from the models explored in the literature, this presentation focuses on the boundary-driven multispecies stirring process on the geometry of a general connected graph. This process is a natural extension of the symmetric exclusion process (SEP) when multiple species of particles are considered. Its dynamics involve the exchange of positions between a particle and a hole or between two colours of particles, both occurring at a rate of 1. In addition to this 'bulk' dynamics, the system is put in contact with boundary reservoirs that inject and remove particles. After describing the process's generator using a suitable representation of the gl(N) Lie algebra, we establish the existence of an absorbing dual process dened on an enlarged graph, in which each boundary is replaced by an absorbing extra-site. This dual process shares the same dynamics in the bulk, but the extra-sites absorb particles, voiding the graph. Considering the integrable version (on a chain with hard-core exclusion) of the multi-species stirring process, we combine absorbing duality and the matrix product ansatz to derive closed expressions for the non-equilibrium steady-state multi-point correlations of the process. Consequently, we formulate exact expressions for the non-equilibrium steady state. Finally, we discuss some extensions to the non-integrable chain. This presentation is based on recent joint work with Rouven Frassek and Cristian Giardinà.

Area: CS18 - Interacting systems in statistical physics II (Chiara Franceschini and Elena Magnanini)

Keywords: multi-species interacting particle systems, integrable systems, non-equilibrium

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