非互易布朗二聚体的最优有限时间控制：热力学异常与多重转变
Optimal Finite-Time Control of Nonreciprocal Brownian Dimers: Thermodynamic Anomaly and Multiple Transitions
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中文总结 AI 辅助
研究非互易相互作用布朗粒子的有限时间热力学最优控制问题，通过操纵粒子对中心和间距求解。发现临界时间及异常，物理正则化可恢复有限最优值并产生转变，有限范围约束下最优协议还有多次转变及功-持续时间扭结。
中文摘要 AI 辅助
我们精确求解了由两个谐振子阱平移的两个非互易相互作用布朗粒子的有限时间热力学最优控制问题。控制器操纵粒子对的中心和间距。非互易相互作用产生内部作用力，耦合这两个通道。最优协议是振荡的，即使目标间距不变也会故意打开二聚体，并能在输运过程中提取功。一个核心发现是存在一个有限临界时间，超过该时间外部功的下限为负无穷：在超过此阈值的任何规定持续时间内，可提取功和输出功率都是无界的。诸如有限阱范围和力饱和等物理正则化恢复了有限最优值，并将异常转化为最优协议转变：在零目标情况下，硬有限范围产生从零协议到最大范围协议的一阶跳跃，而平滑力饱和则产生连续的二阶起始。在有限范围约束下，最优协议可进一步经历多次有限时间转变，产生多个功-持续时间扭结，这在先前研究中没有定性类似物。
英文摘要
We solve exactly a finite-time thermodynamic optimal control problem for two nonreciprocally interacting Brownian particles translated by two harmonic traps. The controller manipulates both the center and separation of the pair. Nonreciprocal interactions generate an internal active force that couples these two channels. The optimal protocol is oscillatory, deliberately opens the dimer even when the target separation is unchanged, and can extract work during transport. A central finding is a finite critical time beyond which the external-work infimum is $-\infty$: at any prescribed duration beyond this threshold, both extractable work and output power are unbounded. Physical regularizations such as finite trap range and force saturation restore a finite optimum and convert the anomaly into optimal-protocol transitions: in the zero-target case, a hard finite range produces a first-order-like jump from the zero protocol to a maximum-range protocol, whereas smooth force saturation gives a continuous, second-order-like onset. Under finite-range constraints, the optimal protocol can further undergo multiple finite-time transitions, producing multiple work-duration kinks with no qualitative analog in prior studies.
