{
  "id": "1401.5244",
  "version": "v2",
  "published": "2014-01-21T09:56:06.000Z",
  "updated": "2015-03-25T09:31:10.000Z",
  "title": "Scaling laws and bulk-boundary decoupling in heat flow",
  "authors": [
    "J. J. del Pozo",
    "P. L. Garrido",
    "P. I. Hurtado"
  ],
  "comment": "5 pages + 5 figures + 3 pages of supplementary material",
  "journal": "Phys. Rev. E 91, 032116 (2015)",
  "doi": "10.1103/PhysRevE.91.032116",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.mtrl-sci",
    "cond-mat.soft",
    "math-ph",
    "math.MP"
  ],
  "abstract": "When driven out of equilibrium by a temperature gradient, fluids respond by developing a nontrivial, inhomogeneous structure according to the governing macroscopic laws. Here we show that such structure obeys strikingly simple scaling laws arbitrarily far from equilibrium, provided that both macroscopic local equilibrium and Fourier's law hold. Extensive simulations of hard disk fluids confirm the scaling laws even under strong temperature gradients, implying that Fourier's law remains valid in this highly nonlinear regime, with putative corrections absorbed into a nonlinear conductivity functional. In addition, our results show that the scaling laws are robust in the presence of strong finite-size effects, hinting at a subtle bulk-boundary decoupling mechanism which enforces the macroscopic laws on the bulk of the finite-sized fluid. This allows to measure for the first time the marginal anomaly of the heat conductivity predicted for hard disks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-21T09:56:06.000Z",
      "title": "Universal scaling laws and bulk-boundary decoupling in fluids out of equilibrium",
      "abstract": "When driven out of equilibrium by a temperature gradient, fluids respond by developing a nontrivial, inhomogeneous structure according to the governing macroscopic laws. Here we show that such structure obeys strikingly simple universal scaling laws arbitrarily far from equilibrium, provided that both macroscopic local equilibrium and Fourier's law hold. These results, that we prove for hard sphere fluids and more generally for systems with homogeneous potentials in arbitrary dimension, are likely to remain valid in the much broader family of strongly correlating fluids where excluded volume interactions are dominant. Extensive simulations of hard disk fluids show that the universal scaling laws are robust even in the presence of strong finite-size effects, via a bulk-boundary decoupling mechanism by which all sorts of spurious finite-size and boundary corrections sum up to renormalize the effective boundary conditions imposed on the bulk fluid, which behaves macroscopically. This allows to measure the properties of macroscopic systems from finite-size simulations.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-03-25T09:31:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.70.Ln",
      "05.40.-a",
      "44.10.+i",
      "65.20.-w"
    ],
    "keywords": [
      "heat flow",
      "bulk-boundary decoupling",
      "scaling laws arbitrarily far",
      "strikingly simple scaling laws",
      "simple scaling laws arbitrarily"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2015,
      "month": "Mar",
      "volume": 91,
      "number": 3,
      "pages": "032116"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015PhRvE..91c2116D"
    }
  }
}