{
  "id": "cond-mat/0205353",
  "version": "v1",
  "published": "2002-05-16T20:38:00.000Z",
  "updated": "2002-05-16T20:38:00.000Z",
  "title": "Exact Large Deviation Functional of a Stationary Open Driven Diffusive System: The Asymmetric Exclusion Process",
  "authors": [
    "B. Derrida",
    "J. L. Lebowitz",
    "E. R. Speer"
  ],
  "comment": "Latex, one PicTeX figure in a separate file",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider the asymmetric exclusion process (ASEP) in one dimension on sites $i = 1,..., N$, in contact at sites $i=1$ and $i=N$ with infinite particle reservoirs at densities $\\rho_a$ and $\\rho_b$. As $\\rho_a$ and $\\rho_b$ are varied, the typical macroscopic steady state density profile $\\bar \\rho(x)$, $x\\in[a,b]$, obtained in the limit $N=L(b-a)\\to\\infty$, exhibits shocks and phase transitions. Here we derive an exact asymptotic expression for the probability of observing an arbitrary macroscopic profile $\\rho(x)$: $P_N(\\{\\rho(x)\\})\\sim\\exp[-L{\\cal F}_{[a,b]}(\\{\\rho(x)\\});\\rho_a,\\rho_b]$, so that ${\\cal F}$ is the large deviation functional, a quantity similar to the free energy of equilibrium systems. We find, as in the symmetric, purely diffusive case $q=1$ (treated in an earlier work), that $\\cal F$ is in general a non-local functional of $\\rho(x)$. Unlike the symmetric case, however, the asymmetric case exhibits ranges of the parameters for which ${\\cal F}(\\{\\rho(x)\\})$ is not convex and others for which ${\\cal F}(\\{\\rho(x)\\})$ has discontinuities in its second derivatives at $\\rho(x) = \\bar{\\rho}(x)$; the fluctuations near $\\bar{\\rho}(x)$ are then non-Gaussian and cannot be calculated from the large deviation function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-05-16T20:38:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary open driven diffusive system",
      "exact large deviation functional",
      "asymmetric exclusion process",
      "macroscopic steady state density"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002cond.mat..5353D"
    }
  }
}