Conflict between fastest relaxation of a Markov process and detailed balance condition
Conflict between fastest relaxation of a Markov process and detailed balance condition
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马尔可夫过程的最快松弛与详细平衡条件之间的冲突
DOI：
10.1103/physreve.93.012129
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发表时间：
2016
影响因子：
2.4
通讯作者：
Kazutaka Takahashi and Masayuki Ohzeki
中科院分区：
文献类型：
--
作者：
中村充宏;早坂和弘;古澤健太郎;諸橋功;関根徳彦;向山敬;田中歌子;Kazutaka Takahashi and Masayuki Ohzeki
我们考虑了马尔可夫动力学的最优化问题，以追求最快地收敛到定态。将该方法应用于有限尺寸系统的连续时间主方程。根据最小作用量原理，得到了转移率矩阵的双臂时程方程。对三态系统进行了显式分析，发现解违反了详细的平衡条件。为了观察解的最优性，对解的性质进行了详细的研究。我们还讨论了马尔可夫动力学的反绝热驱动。然后将转移率矩阵分成两部分，状态由第一部分的本征态给出。第二部分违反了详细平衡条件，起到了反绝热项的作用。
We consider the optimization of Markovian dynamics to pursue the fastest convergence to the stationary state. The brachistochrone method is applied to the continuous-time master equation for finite-size systems. The principle of least action leads to a brachistochrone equation for the transition-rate matrix. Three-state systems are explicitly analyzed, and we find that the solution violates the detailed balance condition. The properties of the solution are studied in detail to observe the optimality of the solution. We also discuss the counterdiabatic driving for the Markovian dynamics. The transition-rate matrix is then divided into two parts, and the state is given by an eigenstate of the first part. The second part violates the detailed balance condition and plays the role of a counterdiabatic term.