{
  "id": "2312.15532",
  "version": "v1",
  "published": "2023-12-24T17:38:15.000Z",
  "updated": "2023-12-24T17:38:15.000Z",
  "title": "Duality for the multispecies stirring process with open boundaries",
  "authors": [
    "Francesco Casini",
    "Rouven Frassek",
    "Cristian Giardinà"
  ],
  "comment": "47 pages, no figures",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We study the stirring process with $N-1$ species on a generic graph $G=(V,\\mathcal{E})$ 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 $\\widetilde{G}=(\\widetilde{V},\\widetilde{\\mathcal{E})}$ which includes additional extra-sites $\\widetilde{V}\\setminus V$ 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-24T17:38:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "open boundaries",
      "dual particles",
      "absorption probabilities",
      "non-equilibrium stationary measure",
      "non-equilibrium steady state"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}