Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge of optimal driving protocols is particularly valuable at the microscale, where energy supply is often limited. Here, we experimentally and theoretically investigate the paradigmatic optimization problem of moving a potential carrying a load through a fluid, in a finite time and over a given distance, in such a way that the required work is minimized. An important step towards more realistic systems is the consideration of memory effects in the surrounding fluid, which are ubiquitous in real-world applications. Therefore, our experiments were performed in viscous and viscoelastic media, which are typical environments for synthetic and biological processes on the microscale. Despite marked differences between the protocols in both fluids, we find that the optimal control protocol and the corresponding average particle trajectory always obey a time-reversal symmetry. We show that this symmetry, which surprisingly applies here to a class of processes far from thermal equilibrium, holds universally for various systems, including active, granular, and long-range correlated media in their linear regimes. The uncovered symmetry provides a rigorous and versatile criterion for optimal control that greatly facilitates the search for energy-efficient transport strategies in a wide range of systems. Using a machine learning algorithm, we demonstrate that the algorithmic exploitation of time-reversal symmetry can significantly enhance the performance of numerical optimization algorithms.

中文翻译：

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微尺度最优控制的通用对称性


优化驱动过程的能源效率可以提供对基础物理的宝贵见解，并且对于从生物过程到机器和机器人的设计等众多应用至关重要。最佳驾驶协议的知识在微观尺度上特别有价值，因为能量供应通常是有限的。在这里，我们通过实验和理论上研究了范式优化问题，即在有限的时间内和给定的距离内通过流体移动承载负载的势能，从而最小化所需的工作。迈向更真实系统的重要一步是考虑周围流体的记忆效应，这在现实世界的应用中普遍存在。因此，我们的实验是在粘性和粘弹性介质中进行的，这是微尺度合成和生物过程的典型环境。尽管两种流体中的协议之间存在显着差异，但我们发现最优控制协议和相应的平均粒子轨迹始终遵循时间反转对称性。我们证明，这种对称性令人惊讶地适用于一类远离热平衡的过程，它普遍适用于各种系统，包括线性状态下的活性、粒状和长程相关介质。未覆盖的对称性为最优控制提供了严格且通用的标准，极大地促进了在各种系统中寻找节能传输策略。使用机器学习算法，我们证明了时间反转对称性的算法利用可以显着提高数值优化算法的性能。