将复杂多维系统的动力学映射到保持平均首次穿越时间的离散状态集上：投影动力学方法
Mapping the dynamics of complex multi-dimensional systems onto a discrete set of states conserving mean first passage times: a Projective Dynamics approach
摘要：
我们考虑任何动力学系统，从一个给定的配置合奏开始，并在时间上发展，直到系统达到一定的固定停止标准，与平均首次通过时间的数量感兴趣。我们提出了一种通用的方法，投影动力学，它映射到一个任意的离散状态${ζ_k}$的系统的多维动态，仅受约束的动态被限制到过渡不超过相邻的状态$ζ_{k\pm 1}$。我们证明了在这个条件下，存在一个主方程，该主方程具有与原动力系统相同的平均第一通过时间的最近邻耦合。我们展示的布朗运动的粒子在一维和二维势能景观和折叠过程的小生物聚合物的方法的应用。我们比较结果的平均第一次通过时间和平均折叠时间得到的投影动力学方法与那些通过直接测量，并在可能的情况下与半解析解。
英文摘要：
We consider any dynamical system that starts from a given ensemble of configurations and evolves in time until the system reaches a certain fixed stopping criterion, with the mean first-passage time the quantity of interest. We present a general method, Projective Dynamics, which maps the multi-dimensional dynamics of the system onto an arbitrary discrete set of states ${ζ_k}$, subject only to the constraint that the dynamics is restricted to transitions not further than the neighboring states $ζ_{k\pm 1}$. We prove that with this imposed condition there exists a master equation with nearest-neighbor coupling with the same mean first-passage time as the original dynamical system. We show applications of the method for Brownian motion of particles in one and two dimensional potential energy landscapes and the folding process of small bio-polymers. We compare results for the mean first passage time and the mean folding time obtained with the Projective Dynamics method with those obtained by a direct measurement, and where possible with a semi-analytical solution.
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