广义力匹配在粗粒化中的几何及其相关信息度量
The geometry of generalized force matching in coarse-graining and related information metrics
AI总结：
本文通过概率条件期望语言重新表述分子系统粗粒化中的力匹配方法为粗观空间的投影，建立力匹配与热力学积分的联系，并提出广义力匹配条件以优化非线性粗粒化映射下的平均势能。
摘要：
我们使用概率语言的条件期望重新表述分子系统粗粒化中的力匹配方法作为粗观空间的投影。这种概率描述的实践结果是将力匹配方法与热力学积分联系起来。这种联系提供了一种系统地构造局部平均力的方法，以通过力匹配最优近似平均势能。我们引入了广义力匹配条件，允许在非线性粗粒化映射（如反应坐标、链的端到端长度）下近似平均势能。此外，我们研究了力匹配与相对熵最小化之间的等价性，并为一般非线性粗粒化映射推导了这一等价性。我们通过分子系统的具体应用详细展示了广义力匹配条件。
英文摘要：
Using the probabilistic language of conditional expectations we reformulate the force matching method for coarse-graining of molecular systems as a projection on spaces of coarse observables. A practical outcome of this probabilistic description is the link of the force matching method with thermodynamic integration. This connection provides a way to systematically construct a local mean force in order to optimally approximate the potential of mean force through force matching. We introduce a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (e.g., reaction coordinates, end-to-end length of chains). Furthermore, we study the equivalence of force matching with relative entropy minimization which we derive for general non-linear coarse graining maps. We present in detail the generalized force matching condition through applications to specific examples in molecular systems.
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