{
  "id": "2305.04562",
  "version": "v1",
  "published": "2023-05-08T09:14:33.000Z",
  "updated": "2023-05-08T09:14:33.000Z",
  "title": "Thermodynamic Trade-off Relation for First Passage Time in Resetting Process",
  "authors": [
    "Priyo Shankar Pal",
    "Arnab Pal",
    "Hyunggyu Park",
    "Jae Sung Lee"
  ],
  "comment": "14 pages, 8 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Resetting is a strategy for boosting the speed of a target-searching process. Since its introduction over a decade ago, most studies have been carried out under the assumption that resetting takes place instantaneously. However, due to its irreversible nature, resetting processes incur a thermodynamic cost, which becomes infinite in case of instantaneous resetting. Here, we take into consideration both the cost and first passage time (FPT) required for a resetting process, in which the reset or return to the initial location is implemented using a trapping potential over a finite but random time period. An iterative generating function and counting functional method \\`a la Feynman and Kac are employed to calculate the FPT and average work for this process. From these results, we obtain an explicit form of the time-cost trade-off relation, which provides the lower bound of the mean FPT for a given work input when the trapping potential is linear. This trade-off relation clearly shows that instantaneous resetting is achievable only when an infinite amount of work is provided. More surprisingly, the trade-off relation derived from the linear potential seems to be valid for a wide range of trapping potentials. In addition, we have also shown that the fixed-time or sharp resetting can further enhance the trade-off relation compared to that of the stochastic resetting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-08T09:14:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first passage time",
      "thermodynamic trade-off relation",
      "resetting process",
      "trapping potential",
      "random time period"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}