Thermodynamic Trade-off Relation for First Passage Time in Resetting Process
| Autor: | Pal, Priyo Shankar, Pal, Arnab, Park, Hyunggyu, Lee, Jae Sung |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 14 pages, 8 figures |
| Databáze: | arXiv |
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