{
  "id": "1901.09815",
  "version": "v1",
  "published": "2019-01-28T17:08:48.000Z",
  "updated": "2019-01-28T17:08:48.000Z",
  "title": "Reaction kinetics in the few-encounter limit",
  "authors": [
    "David Hartich",
    "Aljaz Godec"
  ],
  "comment": "16 pages, 5 figures, submitted to \"Chemical Kinetics Beyond the Textbook\", edited by K. Lindenberg, R. Metzler, G. Oshanin\" (May 2019)",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The classical theory of chemical reactions can be understood in terms of diffusive barrier crossing, where the rate of a reaction is determined by the inverse of the mean first passage time (FPT) to cross a free energy barrier. Whenever a few reaction events suffice to trigger a response or the energy barriers are not high, the mean first passage time alone does not suffice to characterize the kinetics, i.e., the kinetics do not occur on a single time-scale. Instead, the full statistics of the FPT are required. We present a spectral representation of the FPT statistics that allows us to understand and accurately determine FPT distributions over several orders of magnitudes in time. A canonical narrowing of the first passage density is shown to emerge whenever several molecules are searching for the same target, which was termed the 'few-encounter limit'. The few-encounter limit is essential in all situations, in which already the first encounter triggers a response, such as misfolding-triggered aggregation of proteins or protein transcription regulation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-28T17:08:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "few-encounter limit",
      "reaction kinetics",
      "mean first passage time",
      "free energy barrier",
      "reaction events suffice"
    ],
    "tags": [
      "textbook"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}