{
  "id": "2311.15286",
  "version": "v1",
  "published": "2023-11-26T12:57:35.000Z",
  "updated": "2023-11-26T12:57:35.000Z",
  "title": "Macroscopic fluctuation theory of local time in lattice gases",
  "authors": [
    "Naftali R. Smith",
    "Baruch Meerson"
  ],
  "comment": "26 pages, 3 figures",
  "categories": [
    "cond-mat.stat-mech",
    "math.PR"
  ],
  "abstract": "The local time in an ensemble of particles measures the amount of time the particles spend in the vicinity of a given point in space. Here we study fluctuations of this quantity, that is of the empirical time average $R=\\int_{0}^{T}\\rho\\left(x=0,t\\right)\\,dt$ of the density $\\rho\\left(x=0,t\\right)$ at the origin for an initially uniform one-dimensional diffusive lattice gas. We consider both the quenched and annealed initial conditions and employ the Macroscopic Fluctuation Theory (MFT). For a gas of non-interacting random walkers (RWs) the MFT yields exact large-deviation functions of $R$, which are closely related to the ones recently obtained by Burenev \\textit{et al.} (2023) using microscopic calculations for non-interacting Brownian particles. Our MFT calculations, however, additionally yield the most likely history of the gas density $\\rho(x,t)$ conditioned on a given value of $R$. Furthermore, we calculate the variance of the local time fluctuations for arbitrary particle- or energy-conserving diffusive lattice gases. Better known examples of such systems include the simple symmetric exclusion process, the Kipnis-Marchioro-Presutti model and the symmetric zero-range process. Our results for the non-interacting RWs can be readily extended to a step-like initial condition for the density.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-26T12:57:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "macroscopic fluctuation theory",
      "local time",
      "uniform one-dimensional diffusive lattice",
      "one-dimensional diffusive lattice gas",
      "mft yields exact large-deviation functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}