{
  "id": "1905.10260",
  "version": "v1",
  "published": "2019-05-24T14:41:04.000Z",
  "updated": "2019-05-24T14:41:04.000Z",
  "title": "A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension",
  "authors": [
    "Emil Mallmin",
    "Richard A Blythe",
    "Martin R Evans"
  ],
  "comment": "31 pages, 11 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We compare the fluctuations in the velocity and in the fraction of time spent at a given position for minimal models of a passive and an active particle: an asymmetric random walker and a run-and-tumble particle in continuous time and on a 1D lattice. We compute rate functions and effective dynamics conditioned on large deviations for these observables. While generally different, for a unique and non-trivial choice of rates (up to a rescaling of time) the velocity rate functions for the two models become identical, whereas the effective processes generating the fluctuations remain distinct. This equivalence coincides with a remarkable parity of the spectra of the processes' generators. For the occupation-time problem, we show that both the passive and active particles undergo a prototypical dynamical phase transition when the average velocity is non-vanishing in the long-time limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-24T14:41:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "biased diffusion",
      "run-and-tumble dynamics",
      "dynamical fluctuations",
      "comparison",
      "fluctuations remain distinct"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}