扩散动力学的随机作用：重新加权、抽样和最小化
Stochastic actions for diffusive dynamics: Reweighting, sampling, and minimization
摘要：
在扩散动力学的数值研究中，两种不同的作用泛函通常用于指定轨迹的概率分布，其中一种需要评估势的二阶导数以及力。在这里，有人认为，这两个行动是等价的处方的目的，重新加权和采样轨迹，而最可能的路径更一般地给出了全球最小的行动，涉及二阶导数项。这个明显的悖论的答案在于布朗路径的不可微特性，以及与给定轨迹相关的“熵”。
英文摘要：
In numerical studies of diffusive dynamics, two different action functionals are often used to specify the probability distribution of trajectories, one of which requiring the evaluation of the second derivative of the potential in addition to the force. Here it is argued that both actions are equivalent prescriptions for the purposes of reweighting and sampling trajectories, whereas the most probable path is more generally given by the global minimum of the action involving the second derivative term. The answer to this apparent paradox lies in the non-differentiable character of Brownian paths, as well as in the "entropy" associated with a given trajectory.
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