{
  "id": "1407.2065",
  "version": "v2",
  "published": "2014-07-08T12:36:38.000Z",
  "updated": "2015-04-14T18:22:21.000Z",
  "title": "Fluctuating Currents in Stochastic Thermodynamics I. Gauge Invariance of Asymptotic Statistics",
  "authors": [
    "Artur Wachtel",
    "Jürgen Vollmer",
    "Bernhard Altaner"
  ],
  "comment": "An accompanying publication \"Fluctuating Currents in Stochastic Thermodynamics II. Energy Conversion and Nonequilibrium Response in Kinesin Models\" by the same authors is also available on the arXiv",
  "categories": [
    "cond-mat.stat-mech",
    "physics.bio-ph"
  ],
  "abstract": "Stochastic Thermodynamics uses Markovian jump processes to model random transitions between observable mesoscopic states. Physical currents are obtained from anti-symmetric jump observables defined on the edges of the graph representing the network of states. The asymptotic statistics of such currents are characterized by scaled cumulants. In the present work, we use the algebraic and topological structure of Markovian models to prove a gauge invariance of the scaled cumulant-generating function. Exploiting this invariance yields an efficient algorithm for practical calculations of asymptotic averages and correlation integrals. We discuss how our approach generalizes the Schnakenberg decomposition of the average entropy-production rate, and how it unifies previous work. The application of our results to concrete models is presented in an accompanying publication.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-08T12:36:38.000Z",
      "title": "Determining the Statistics of Fluctuating Currents: General Markovian Dynamics and its Application to Motor Proteins",
      "abstract": "Fluctuations in biological systems are commonly modeled by Markovian jump processes. Here we present a method for the analytical calculation of the fluctuation spectrum for any fluctuating physical current -- without need to solve for the steady-state probability distribution. Our result provides a generalization of the Schnakenberg decomposition for currents to their fluctuation spectrum at arbitrary order. The decomposition shows that topological cycles in the system fully characterize the steady-state statistics. For the biochemical motor protein kinesin our method reproduces previous results via considerably less involved calculations, and it unveils previously hidden features of the models.",
      "comment": "27 pages, 13 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-14T18:22:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.70.Ln",
      "87.10.Mn",
      "02.50.Ga",
      "87.15.A-"
    ],
    "keywords": [
      "general markovian dynamics",
      "fluctuating currents",
      "statistics",
      "fluctuation spectrum",
      "application"
    ],
    "publication": {
      "doi": "10.1103/PhysRevE.92.042132",
      "journal": "Physical Review E",
      "year": 2015,
      "month": "Oct",
      "volume": 92,
      "number": 4,
      "pages": "042132"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015PhRvE..92d2132W"
    }
  }
}