AI 中文总结
研究可逆系统热弛豫问题，发现全开门策略虽在多方面最优，但存在违反直觉的有限时间最优解，即利用非对易性通过本征向量旋转和反向门控实现更快弛豫，还给出不可行定理及逆问题结果，势垒控制只重排耗散预算。
AI 中文摘要
对于一个弛豫到平衡态的可逆系统，直观上最快的策略是降低所有动力学势垒（打开所有门）。我们发现这种直觉在三个层面成立：全开门策略实现了最高的局部电导，在每个$f$散度中使瞬时趋近速度最大化，并同时使所有弛豫本征值最大化。然而，我们表明一个违反直觉的有限时间最优解超出了这种直觉，在第四个层面起作用，前三个层面无法察觉：本征向量旋转。非对易性使时间调度能够在弛豫模式间重新投影残余振幅，从而实现更快的弛豫。最优调度是开关式的。在我们的示例中，找到的最佳调度还采用了反向门控，即瞬时提高选定的势垒，相对于全开门，终端残余减少了130倍，相对于最佳静态态势减少了7倍。一个不可行定理表明非对易性是必要条件：对易生成元会使每个调度退化为静态时间平均态势，比直观的静态控制更差。在逆问题中，对偶调度比直观地将所有势垒保持在最大高度更有效地保持非平衡自由能。无论加速还是延迟弛豫，势垒控制对简化的马尔可夫系统不做功；它只是重新安排固定的总耗散预算。
英文摘要
For a reversible system relaxing to equilibrium, the obvious fastest strategy is to lower all kinetic barriers (open all gates). We find that such intuition holds at three levels: the all-open-gate strategy achieves the highest local conductance, it maximizes the instantaneous speed of approach in every $f$-divergence, and it simultaneously maximizes all relaxation eigenvalues. Nevertheless, we show that a counter-intuitive finite-time optimum lies beyond this intuition and operates at a fourth level, invisible to all three: eigenvector rotation. Noncommutativity enables timed schedules to reproject residual amplitudes across relaxation modes, thereby achieving faster relaxation. Optimal schedules are bang--bang. In our illustrative example, the best-found schedule also employs counter-gating, transiently raising selected barriers, and reduces the terminal residual by a factor of $130$ relative to all-open, and by $7$ relative to the best static landscape. A no-go theorem shows that noncommutativity is necessary: commuting generators collapse every schedule to a static time-averaged landscape, worse than the intuitive static control. In the reverse problem, the dual schedule preserves nonequilibrium free energy far more effectively than intuitively keeping all barriers at maximum heights. Whether accelerating or delaying relaxation, barrier control performs no work on the reduced Markov system; it only re-times a fixed total dissipation budget.
