Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic equations of motion, introduces time into the description of thermodynamic processes—which opens the way to fine control them. As a result, the field of finite-time thermodynamics of mesoscopic systems has blossomed. In this article, after introducing a few concepts of control for isolated mechanical systems evolving according to deterministic equations of motion, we review the different strategies that have been developed to realize finite-time state-to-state transformations in both over and underdamped regimes, by the proper design of time-dependent control parameters/driving. The systems under study are stochastic, epitomized by a Brownian object immersed in a fluid; they are thus strongly coupled to their environment playing the role of a reservoir. Interestingly, a few of those methods (inverse engineering, counterdiabatic driving, fast-forward) are directly inspired by their counterpart in quantum control. The review also analyzes the control through reservoir engineering. Besides the reachability of a given target state from a known initial state, the question of the optimal path is discussed. Optimality is here defined with respect to a cost function, a subject intimately related to the field of information thermodynamics and the question of speed limit. Another natural extension discussed deals with the connection between arbitrary states or non-equilibrium steady states. This field of control in stochastic thermodynamics enjoys a wealth of applications, ranging from optimal mesoscopic heat engines to population control in biological systems.

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在保持控制的同时快速驾驶：从哈密顿量到随机动力学的经典捷径

随机热力学建立了一个广泛的框架，以重新审视介观系统的单个随机轨迹的热、功和熵产生的古老概念。值得注意的是，这种方法依赖于随机运动方程，将时间引入热力学过程的描述中——这为精细控制它们开辟了道路。结果，介观系统的有限时间热力学领域蓬勃发展。在这篇文章中，在介绍了根据确定性运动方程演化的孤立机械系统的一些控制概念之后，我们回顾了为实现过阻尼和欠阻尼状态下的有限时间状态到状态转换而开发的不同策略，通过适当设计时间相关的控制参数/驱动。所研究的系统是随机的，以浸入流体中的布朗物体为代表；因此，它们与环境紧密耦合，扮演着水库的角色。有趣的是，其中一些方法（逆向工程、反绝热驱动、快进）直接受到量子控制中对应方法的启发。该评论还分析了通过油藏工程进行的控制。除了从已知初始状态到给定目标状态的可达性之外，还讨论了最佳路径的问题。这里的最优性是根据成本函数定义的，这是一个与信息热力学领域和速度限制问题密切相关的主题。讨论的另一个自然扩展涉及任意状态或非平衡稳态之间的联系。