标题： 时间-能量权衡在使用最优控制的随机重置中的应用 显示英文标题

标题： Time-energy tradeoff in stochastic resetting using optimal control

摘要： 随机重置是一种已知可以最小化达到目标的首次通过时间的驱动机制，但需要消耗能量。 每个重置事件的物理实现的选择决定了搜索过程加速与能量消耗之间的权衡。 在这里，我们提出了一种最优传输协议，该协议平衡了每次重置事件的持续时间和能量消耗。 该协议在有限时间内以最小的能量消耗将谐波束缚的布朗粒子从一个平衡状态驱动到另一个平衡状态。 与其他类型的有限时间协议进行明确比较进一步显示了其特定的热力学特性。 其成本既是未优化捷径协议成本的下限，也是不保证最终平衡的最优协议成本的上限。 当将最优传输协议应用于实现随机重置时，达到了单一的最低时间-能量界限：该协议允许在能量消耗和搜索时间之间达到最佳权衡。 显示英文摘要

摘要： Stochastic resetting is a driving mechanism that is known to minimize the first passage time to reach a target, at the cost of energy expenditure. The choice of the physical implementation of each resetting event determines the tradeoff between the acceleration of the search process and its energetic cost. Here, we present an optimal transport protocol that balances the duration and the energetic cost of each resetting event. This protocol drives a harmonically trapped Brownian particle between two equilibrium states within a finite time and with minimal energetic cost. An explicit comparison with other types of finite-time protocols further shows its specific thermodynamic properties. Its cost is both a lower bound on the cost of unoptimized shortcut protocols and an upper bound on the cost of optimal protocols which do not ensure final equilibrium. When applying the optimal transport protocol to implement stochastic resetting, a single lower time-energy bound is reached: this protocol allows to reach the best tradeoff between energetic cost and search time.