论文标题
在有限时间内实现膜分离的最低能量费用的测地界结合
Geodesic bound of the minimum energy expense to achieve membrane separation within finite time
论文作者
论文摘要
要在有限的操作时间内完成任务，通常需要过多的能源费用，其最小值对于各种应用中的最佳设计至关重要，尤其是在纯化组件净化的混合物的工业分离中。已经取得了技术进步来实现更好的纯化，而能源费用较低，但对于有限的运行时间中超量能源费用的基本限制知之甚少。我们得出了这样的限制，并显示了其与初始状态和最终状态之间的几何距离的平方以及与操作时间$τ$相反的平方。我们的结果表明，优化分离协议等同于在几何空间中找到大地测量曲线。有趣的是，我们通过最小能量费用显示了最佳控制，可以通过破坏对称的协议来实现，在这种方案中，这两个膜以不同的速度彼此移动。
To accomplish a task within limited operation time typically requires an excess expense of energy, whose minimum is of practical importance for the optimal design in various applications, especially in the industrial separation of mixtures for purification of components. Technological progress has been made to achieve better purification with lower energy expense, yet little is known about the fundamental limit on the least excess energy expense in finite operation time. We derive such a limit and show its proportionality to the square of a geometric distance between the initial and final states and inverse proportionality to the operation time $τ$. Our result demonstrates that optimizing the separation protocol is equivalent to finding the geodesic curve in a geometric space. Interestingly, we show the optimal control with the minimum energy expense is achieved by a symmetry-breaking protocol, where the two membranes are moved toward each other with different speeds.
