Free-energy difference calculations based on atomistic simulations generally improve in accuracy when sampling from a sequence of intermediate equilibrium thermodynamic states that bridge the configuration space between two states of interest. For reasons of efficiency, usually the same samples are used to calculate the stepwise difference of such an intermediate to both adjacent intermediates. However, this procedure violates the assumption of uncorrelated estimates that is necessary to derive both the optimal sequence of intermediate states and the widely used Bennett acceptance ratio estimator. In this work, via a variational approach, we derive the sequence of intermediate states and the corresponding estimator with minimal mean-squared error that account for these correlations and assess its accuracy.

中文翻译：

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中间状态之间相关自由能估计的变分中间体

从一系列中间平衡热力学状态采样时，基于原子模拟的自由能差计算通常会提高准确性，这些中间平衡热力学状态桥接了两个感兴趣状态之间的构型空间。由于效率的原因，通常使用相同的样本来计算这种中间体与两个相邻中间体的逐步差异。但是，此过程违反了不相关估计的假设，该假设是导出中间状态的最佳序列和广泛使用的Bennett接受率估计器所必需的。在这项工作中，通过变分方法，我们得出了中间状态的序列以及具有最小均方误差的对应估计量，这些均值误差解释了这些相关性并评估了其准确性。