English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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 outunder the assumption that resetting takes place instantaneously. However, dueto its irreversible nature, resetting processes incur a thermodynamic cost,which becomes infinite in case of instantaneous resetting. Here, we take intoconsideration both the cost and first passage time (FPT) required for aresetting process, in which the reset or return to the initial location isimplemented using a trapping potential over a finite but random time period. Aniterative generating function and counting functional method \`a la Feynman andKac are employed to calculate the FPT and average work for this process. Fromthese 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 thetrapping potential is linear. This trade-off relation clearly shows thatinstantaneous resetting is achievable only when an infinite amount of work isprovided. More surprisingly, the trade-off relation derived from the linearpotential seems to be valid for a wide range of trapping potentials. Inaddition, we have also shown that the fixed-time or sharp resetting can furtherenhance the trade-off relation compared to that of the stochastic resetting.

Thermodynamic Trade-off Relation for First Passage Time in Resetting Process