Dynamical Emergence Principle of Reaction Selectivity and Molecular Memory in Chemical Reactions' and Biomolecular Systems

不返回过渡态（TS）定义在多维相空间中，其中通过常用的“配置”TS通过一次的recrossing轨迹，鲁棒地存在到反应阈值以上的适度高的能量制度，即使当浴自由度之间的非线性共振垂直于反应坐标导致局部混沌。然而，在更高的能量，当整体混沌出现在浴空间，从浴自由度的反应坐标的可分性停止举行局部。在鞍点附近的相空间中，发现系统越慢通过TS，越多的轨迹重现。讨论了它们的意义和机制，讨论了在反应阈值以上的高能区如何定义不返回TS，并发展了一个新的经验自洽方案，从短的单分子时间序列系综中阐明局域遍历态分布函数和构造有效的多维自由能景观.我们有可能捕捉到的不是多维自由能景观的整个地形，而是系统经常漫游的区域。利用局域遍历性作为0^<th>阶描述，我们构造了多维“自由能”景观，其中几个局域遍历态通过引入它们之间的“距离”而联系在一起。通过对单分子时间序列系综中跃迁序列的概率估计，可以分析沿沿着多条跃迁路径的非马尔可夫性。例如，在一个实施例中，记忆和过渡路径长度之间的关系。作为n_s时间窗的函数来估计短时分布，我们还可以分配时间n_s内可到达的超盆（一组状态）的数量。

No-return transition states (TSs) defined in multidimensional phase space, where recrossing trajectories through the commonly used ‘configuration' TS pass only once, robustly exist up to moderately high energy regime above the reaction threshold even when nonlinear resonances among the bath degrees of freedom perpendicular to the reaction coordinate result in local chaos. However, at much higher energy when global chaos appears in the bath space, the separability of the reaction coordinate from the bath degrees of freedom ceases to hold locally. In the phase space near the saddles, it is found that the slower the system passes the TS, the more recrossing trajectories reappear. Their implications and mechanisms are discussed concerning to what extent one can define no-return TSs in high energy regime above the reaction threshold.We also developed a new empirical self-consistent scheme to elucidate the local ergodic state distribution function and construct effective multidimensional free energy landscape from an ensemble of short single molecule time series. It is possible to capture not the entire topography of the multidimensional free energy landscape but the regions where the system wanders frequently. Using local ergodicity ansatz as a 0^<th> order description, we constructed the multidimensional "free energy" landscape where several local ergodic states are linked with introducing a "distance" among them. Evaluating on the probability of transition sequences sampled in an ensemble of single molecule time series, one can analyze non-Markovianity along several transition paths. e.g., relationship between memory and length of transition paths. As a function of n_s time window to estimate the short time distribution, we can also assign the number of accessible superbasins (a set of states) within time n_s.