庞特里亚金原理在布朗粒子工程平衡中的应用
An application of Pontryagin's principle to Brownian particle engineered equilibration
摘要：
我们提出了一个程式化的控制平衡的一个小系统在波动的环境。我们推导出了控制最优控制的方程，使系统在两个平衡态之间转向\emph{in finite time}。相应的热力学过渡是最佳的意义上说，发生在最小熵，如果允许的控制集是由一定的界限上的时间导数的协议的限制。我们将我们的方程的工程平衡的光阱考虑在最近的原理实验证明。我们还分析了一个基本模型的成核先前考虑的Landauer讨论的热力学成本的一位信息擦除。我们希望我们的模型是一个有用的基准实验设计，因为它具有相同的可积性的最佳质量传输的可压缩速度场的知名模型。
英文摘要：
We present a stylized model of controlled equilibration of a small system in a fluctuating environment. We derive the equations governing the optimal control steering \emph{in finite time} the system between two equilibrium states. The corresponding thermodynamic transition is optimal in the sense that occurs at minimum entropy if the set of admissible controls is restricted by certain bounds on the time derivatives of the protocols. We apply our equations to the engineered equilibration of an optical trap considered in a recent proof of principle experiment. We also analyze an elementary model of nucleation previously considered by Landauer to discuss the thermodynamic cost of one bit of information erasure. We expect our model to be a useful benchmark for experiment design as it exhibits the same integrability properties of well known models of optimal mass transport by a compressible velocity field.
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