论文标题
拓扑速度限制
Topological Speed Limit
论文作者
论文摘要
任何物理系统都以有限速度发展，不仅受到能量成本的约束，而且还受到基础动力学的拓扑结构的约束。在这封信中，通过考虑此类结构信息，我们使用最佳运输方法得出了物理状态进化的统一拓扑速度限制。我们证明，改变状态所需的最小时间是由离散的瓦斯坦距离限制的，该距离编码系统的拓扑信息以及时间平均速度。获得的结合是紧密的，适用于从确定性到随机性以及经典到量子系统的广泛动力学。此外，边界还提供了对达到最大速度的最佳过程的设计原理的见解。我们证明了我们的结果在化学反应网络中的应用和相互作用的多体量子系统。
Any physical system evolves at a finite speed that is constrained not only by the energetic cost but also by the topological structure of the underlying dynamics. In this Letter, by considering such structural information, we derive a unified topological speed limit for the evolution of physical states using an optimal transport approach. We prove that the minimum time required for changing states is lower bounded by the discrete Wasserstein distance, which encodes the topological information of the system, and the time-averaged velocity. The bound obtained is tight and applicable to a wide range of dynamics, from deterministic to stochastic, and classical to quantum systems. In addition, the bound provides insight into the design principles of the optimal process that attains the maximum speed. We demonstrate the application of our results to chemical reaction networks and interacting many-body quantum systems.
