Graduate School of China Academy of Engineering Physics, Beijing 100193, China.
Beijing Computational Science Research Center, Beijing 100193, China.
Phys Rev E. 2023 Jan;107(1-1):014103. doi: 10.1103/PhysRevE.107.014103.
Accelerating controlled thermodynamic processes requires an auxiliary Hamiltonian to steer the system into instantaneous equilibrium states. An extra energy cost is inevitably needed in such finite-time operation. We recently developed a geodesic approach to minimize such energy cost for the shortcut to isothermal process. The auxiliary control typically contains momentum-dependent terms, which are hard to be experimentally implemented due to the requirement of constantly monitoring the speed. In this work, we employ a variational auxiliary control without the momentum-dependent force to approximate the exact control. Following the geometric approach, we obtain the optimal control protocol with variational minimum energy cost. We demonstrate the construction of such protocol via an example of Brownian motion with a controllable harmonic potential.
加速受控热力学过程需要辅助哈密顿量来引导系统进入瞬时平衡态。在这种有限时间操作中，不可避免地需要额外的能量成本。我们最近开发了一种测地线方法来最小化这种能量成本，以实现等温过程的捷径。辅助控制通常包含与动量相关的项，由于需要不断监测速度，因此很难在实验中实现。在这项工作中，我们使用没有与动量相关的力的变分辅助控制来近似精确控制。遵循几何方法，我们得到了具有变分最小能量成本的最优控制协议。我们通过可控谐波势的布朗运动的例子展示了这种协议的构建。
