标题： 一般阻尼布朗热机的最优约束控制 显示英文标题

标题： Optimal constrained control for generally damped Brownian heat engines

摘要： 循环随机热机的优化，这一研究领域跨越数十年，通常假设在循环的离散点上控制参数或响应参数是固定的——这种限制往往导致实验上难以实现的操作方案。 我们通过一种从最优控制理论改编而来的通用算法克服了这一问题，该算法在现实约束下（例如刚度和温度限制）优化整个循环的动力学，适用于各种系统。 与依赖固定端点且不适合无约束循环的几何方法或质量输运方法不同，我们的方法同时调整循环时间和控制变化。 应用于一个在谐振势中的普遍阻尼布朗粒子——一个实验相关的案例——我们的方法在过阻尼情况下得到验证，并扩展到任意阻尼率。 随着阻尼减小，最大功率消失且循环时间发散；在固定循环时间下，效率也呈现出类似的趋势，最优操作方案表现出非单调的复杂性。 值得注意的是，优化温度剖面——通常被忽视——显著提高了中间阻尼范围内的效率。 我们的工作建立了第一个在实验约束下优化循环随机过程的系统框架，拓宽了非平衡热力学中功率和效率优化的范围。 显示英文摘要

摘要： Optimization of cyclic stochastic heat engines, a topic spanning decades of research, commonly assumes fixed control or response parameters at discrete points in the cycle-a limitation that often leads to experimentally impractical protocols. We overcome this with a general algorithm, adapted from optimal control theory, that optimizes full-cycle dynamics under realistic constraints, such as stiffness and temperature bounds, across diverse systems. Unlike geometric or mass transport methods, which rely on fixed endpoints and are unsuitable for unconstrained cycles, our approach simultaneously tunes both cycle time and control variations. Applied to a generally damped Brownian particle in a harmonic potential-an experimentally relevant case-our method is validated in the overdamped regime and extended to arbitrary damping rates. As damping decreases, maximum power vanishes and cycle time diverges; at fixed cycle times, efficiency follows a similar trend, with optimal protocols exhibiting non-monotonic complexity. Notably, optimizing temperature profiles-often overlooked-significantly enhances efficiency in intermediate damping regimes. Our work establishes the first systematic framework for optimizing cyclic stochastic processes under experimental constraints, broadening the scope of power and efficiency optimization in nonequilibrium thermodynamics.