具有随机返回的扩散过程的新兴成本-时间 Pareto 前沿
Emerging cost-time Pareto front for diffusion with stochastic return
AI总结：
本文利用带外部限制陷阱的随机返回协议对扩散粒子进行热力学分析，发现在给定平均做功下可找到最小化期望首达时间的最优势能形状，揭示了首达时间与做功之间的 Pareto 权衡关系。
摘要：
重置——即系统在固定或随机时间后被定期返回到给定状态——已成为优化系统搜索性能的有效策略。早期理论框架主要关注瞬时重置（系统被直接传送至给定状态），但涉及有限返回时间的物理重置机制正引起越来越多的关注。然而，采用此类机制需要付出成本，且该成本对搜索时间的影响在很大程度上尚未被探索。为了设计高性价比的重置策略，回答这一问题至关重要。受此启发，我们利用带有外部限制陷阱的随机返回协议，对粒子位置被间歇性重置至特定位点的扩散粒子进行了热力学分析。我们证明，对于一族满足 $U_R(x) \sim |x|^{m}$（其中 $m>0$）的势能，能够找到在给定热力学成本（即平均做功）下使期望首达时间最小化的最优势能形状。通过改变该成本值，我们获得了 Pareto 最优前沿，并证明了首达时间与所做功之间的权衡关系。
英文摘要：
Resetting, in which a system is regularly returned to a given state after a fixed or random duration, has become a useful strategy to optimize the search performance of a system. While earlier theoretical frameworks focused on instantaneous resetting, wherein the system is directly teleported to a given state, there is a growing interest in physical resetting mechanisms that involve a finite return time. However employing such a mechanism involves cost and the effect of this cost on the search time remains largely unexplored. Yet answering this is important in order to design cost-efficient resetting strategies. Motivated from this, we present a thermodynamic analysis of a diffusing particle whose position is intermittently reset to a specific site by employing a stochastic return protocol with external confining trap. We show for a family of potentials $U_R(x) \sim |x|^{m}$ with $m>0$, it is possible to find optimal potential shape that minimises the expected first-passage time for a given value of the thermodynamic cost, i.e. mean work. By varying this value, we then obtain the Pareto optimal front, and demonstrate a trade-off relation between the first-passage time and the work done.
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