Suppression of work fluctuations by optimal control: An approach based on Jarzynski's equality.
Suppression of work fluctuations by optimal control: An approach based on Jarzynski's equality.
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DOI：
10.1103/physreve.90.052132
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发表时间：
2014-08
期刊：
影响因子：
--
通讯作者：
G. Xiao;J. Gong
中科院分区：
文献类型：
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作者：
G. Xiao;J. Gong
理解和操纵微尺度和纳米尺度系统的功波动既有基础意义又有实际意义。例如，功波动方面将是设计纳米级热机的一个重要因素。在这项工作中，提出了一种直接利用Jarzynski等式的最优控制方法，以有效地抑制系统（最初处于热平衡状态）在工作协议下但在协议期间与浴池隔离的功统计量的波动。控制策略是最小化e^{-βW}的单个值与e^{-βΔF}给出的整体平均值的偏差，其中W是功，β是逆温度，ΔF是两个平衡态之间的自由能差。进一步表明，即使在系统哈密顿量不完全已知的情况下，通过Jarzynski等式本身动态地改进控制目标函数，仍然可以通过反馈回路抑制功的波动。数值实验基于线性和非线性参数振子。线性参数振荡器的最优控制结果也与基于绝热捷径的早期结果进行了基准测试。
Understanding and manipulating work fluctuations in microscale and nanoscale systems are of both fundamental and practical interest. For example, aspects of work fluctuations will be an important factor in designing nanoscale heat engines. In this work, an optimal control approach directly exploiting Jarzynski's equality is proposed to effectively suppress the fluctuations in the work statistics, for systems (initially at thermal equilibrium) subject to a work protocol but isolated from a bath during the protocol. The control strategy is to minimize the deviations of individual values of e^{-βW} from their ensemble average given by e^{-βΔF}, where W is the work, β is the inverse temperature, and ΔF is the free energy difference between two equilibrium states. It is further shown that even when the system Hamiltonian is not fully known, it is still possible to suppress work fluctuations through a feedback loop, by refining the control target function on the fly through Jarzynski's equality itself. Numerical experiments are based on linear and nonlinear parametric oscillators. Optimal control results for linear parametric oscillators are also benchmarked with early results based on shortcuts to adiabaticity.