δ函数脉冲对于快速驱动的惯性随机系统是最优的
Delta-Function Kicks are Optimal for Rapidly Driven Inertial Stochastic Systems
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中文总结 AI 辅助
研究人员通过短时近似证明，δ函数脉冲是一般约束下惯性随机系统（含主动、量子动力学）最小化耗散的最优控制手段，可使功随短协议时长呈线性缩放，短时极限下节省功的比值发散。
中文摘要 AI 辅助
最优控制有助于深化我们对随机热力学的理解，进而推导出普适性质与几何表述。在最优控制最初那些令人惊讶的性质中，不仅离散跳变，δ函数脉冲也被证明是特定示例系统中最小化耗散所必需的。利用短时近似，本文表明δ函数脉冲对于最小化惯性随机系统的耗散具有普适最优性，包括一般约束下的主动动力学与量子动力学。从根本上源于基础运动学，δ函数脉冲是实现功随短协议时长呈线性缩放的必要条件，而无此类脉冲时功呈二次缩放。这意味着在短时极限下，节省的功的比值会发散（趋于无穷）。
英文摘要
Optimal control helps guide our understanding of stochastic thermodynamics, leading to universal properties and geometric formulations. Among the initially surprising properties of optimal control, not only discrete jumps but delta function kicks have been shown to be necessary to minimize dissipation in specific example systems. Using a short-time approximation, I show that delta-function kicks are universally optimal for minimizing dissipation in inertial stochastic systems, including active and quantum dynamics under general constraints. Fundamentally stemming from basic kinematics, delta-function kicks are required to achieve linear scaling of work with short protocol durations compared to the quadratic scaling without the kicks. This implies a diverging (infinite) ratio of saved work in the short-time limit.
