{
  "id": "1202.0508",
  "version": "v1",
  "published": "2012-02-02T18:12:35.000Z",
  "updated": "2012-02-02T18:12:35.000Z",
  "title": "Non-equilibrium and information: the role of cross-correlations",
  "authors": [
    "Andrea Crisanti",
    "Andrea Puglisi",
    "Dario Villamaina"
  ],
  "comment": "30 pages, 4 figures, 4 appendixes",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We discuss the relevance of information contained in cross-correlations among different degrees of freedom, which is crucial in non-equilibrium systems. In particular we consider a stochastic system where two degrees of freedom $X_1$ and $X_2$ - in contact with two different thermostats - are coupled together. The production of entropy and the violation of equilibrium fluctuation-dissipation theorem (FDT) are both related to the cross-correlation between $X_1$ and $X_2$. Information about such cross-correlation may be lost when single-variable reduced models, for $X_1$, are considered. Two different procedures are typically applied: (a) one totally ignores the coupling with $X_2$; (b) one models the effect of $X_2$ as an average memory effect, obtaining a generalized Langevin equation. In case (a) discrepancies between the system and the model appear both in entropy production and linear response; the latter can be exploited to define effective temperatures, but those are meaningful only when time-scales are well separated. In case (b) linear response of the model well reproduces that of the system; however the loss of information is reflected in a loss of entropy production. When only linear forces are present, such a reduction is dramatic and makes the average entropy production vanish, posing problems in interpreting FDT violations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-02T18:12:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.70.-a",
      "05.10.Gg"
    ],
    "keywords": [
      "cross-correlation",
      "information",
      "linear response",
      "equilibrium fluctuation-dissipation theorem",
      "average memory effect"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevE.85.061127",
      "journal": "Physical Review E",
      "year": 2012,
      "month": "Jun",
      "volume": 85,
      "number": 6,
      "pages": "061127"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012PhRvE..85f1127C"
    }
  }
}