标题： 耗散朗之万系统中熵产生下限的正态分布分析 显示英文标题

标题： Lower Bound of Entropy Production in an Underdamped Langevin System with Normal Distributions

摘要： 我们研究了一维欠阻尼朗之万系统在时间依赖的抛物势约束下的熵产生下限。 我们专注于在给定初始分布到给定最终分布并花费给定有限时间的过渡过程中最小化熵产生。 我们利用均值和协方差矩阵的演化方程，推导出实现最小熵产生的条件，以确定刚度和势能中心的最优控制协议。 我们的研究结果表明，由于控制协议的限制，并非所有的协方差矩阵都可以作为初始和最终条件。 这项研究将现有对过阻尼系统的知识扩展到了欠阻尼系统。 显示英文摘要

摘要： We study the lower bound of the entropy production in a one-dimensional underdamped Langevin system constrained by a time-dependent parabolic potential. We focus on minimizing the entropy production during transitions from a given initial distribution to a given final distribution taking a given finite time. We derive the conditions for achieving the minimum entropy production for the processes with normal distributions, using the evolution equations of the mean and covariance matrix to determine the optimal control protocols for stiffness and center of the potential. Our findings reveal that not all covariance matrices can be given as the initial and final conditions due to the limitations of the control protocol. This study extends existing knowledge of the overdamped systems to the underdamped systems.