Effective dynamics using conditional expectations
Effective dynamics using conditional expectations
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DOI：
10.1088/0951-7715/23/9/006
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发表时间：
2010-09-01
期刊：
影响因子：
1.7
通讯作者：
Lelievre, Tony
中科院分区：
文献类型：
--
作者：
Legoll, Frederic;Lelievre, Tony
粗粒化问题在分子动力学中是普遍存在的。在本文中，我们感兴趣的是推导出一个粗粒度变量xi（x）的动力学的有效性质，其中x描述了系统在高维空间Rn中的配置，xi是一个给定的光滑函数，其值在R（通常是反应坐标）中。众所周知，给定x上的玻尔兹曼-吉布斯分布是Rn的元素，xi（x）上的平衡性质完全由自由能决定。另一方面，xi（x）上的有效动力学问题要难得多。从x是Rn中的一个元素的过阻尼Langevin方程出发，我们提出了xi（x）的一个有效动力学.有条件的期望。利用熵的方法，我们给出了充分条件的时间边缘的有效动态接近原来的，精确的误差界。我们检查数值上的几个例子，这些充分条件产生一个有效的动力学，准确地再现了在势能威尔斯的停留时间。我们还讨论了在路径意义上的有效动力学的准确性，以及自由能的相关性，以建立一个粗粒度的动态。
The question of coarse-graining is ubiquitous in molecular dynamics. In this paper, we are interested in deriving effective properties for the dynamics of a coarse-grained variable xi(x), where x describes the configuration of the system in a high-dimensional space R-n, and xi is a given smooth function with value in R (typically a reaction coordinate). It is well known that, given a Boltzmann-Gibbs distribution on x is an element of R-n, the equilibrium properties on xi(x) are completely determined by the free energy. On the other hand, the question of the effective dynamics on xi(x) is much more difficult to address. Starting from an overdamped Langevin equation on x is an element of R-n, we propose an effective dynamics for xi(x). Rusing conditional expectations. Using entropy methods, we give sufficient conditions for the time marginals of the effective dynamics to be close to the original ones, with precise error bounds. We check numerically on several examples that these sufficient conditions yield an effective dynamics which accurately reproduces the residence times in the potential energy wells. We also discuss the accuracy of the effective dynamics in a pathwise sense, and the relevance of the free energy to build a coarse-grained dynamics.