{
  "id": "1803.05609",
  "version": "v1",
  "published": "2018-03-15T06:08:28.000Z",
  "updated": "2018-03-15T06:08:28.000Z",
  "title": "Hydrodynamic Limit of the Inhomogeneous $\\ell$-TASEP with Open Boundaries: Derivation and Solution",
  "authors": [
    "Dan D. Erdmann-Pham",
    "Khanh Dao Duc",
    "Yun S. Song"
  ],
  "comment": "19 pages, 8 figures, 1 table",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.MP",
    "math.PR"
  ],
  "abstract": "The totally asymmetric simple exclusion process, which describes the transport of interacting particles in a lattice, has been actively studied over the past several decades. For general cases where particles have an extended size and hop at site-dependent rates, however, theoretically analyzing the dynamics has remained elusive. Here, we present such an analysis by deriving and solving the hydrodynamic limit. We obtain closed-form formulas for steady-state particle densities and currents, as well as phase transition boundaries. Surprisingly the latter depend on only four parameters: the particle size and the first, the last, and the minimum hopping rates. Our results agree well with Monte Carlo simulations and can be used in inference.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-15T06:08:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hydrodynamic limit",
      "open boundaries",
      "totally asymmetric simple exclusion process",
      "derivation",
      "phase transition boundaries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}