How many trials should you expect to perform to estimate a free-energy difference ?
How many trials should you expect to perform to estimate a free-energy difference ?
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您应该进行多少次试验来估计自由能差异？
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
C. Jarzynski
中科院分区：
文献类型：
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作者：
Nicole Yunger Halpern;C. Jarzynski
自由能之间的差异 ΔF 在生物学、化学和药理学中都有应用。 ΔF 的值可以通过统计力学中开发的波动定理从实验或模拟中估计出来。计算 (ΔF ) 估计中的误差很困难。更糟糕的是，非典型试验主导了估计。 [1] 中粗略估计了应该进行多少次试验。我们用信息论策略增强近似：我们用实验者或模拟器选择的容差参数来量化“优势”。我们使用 ∞ 阶 Rényi 熵来限制人们应该执行的试验数量。如果实施双向性的“良好实践”（已知可以改进 ΔF 的估计），则可以估计界限。根据此次数的试验估计 ΔF 会导致我们近似限制的误差。弱相互作用稀经典气体的数值实验支持我们的分析计算。
The difference ∆F between free energies has applications in biology, chemistry, and pharmacology. The value of ∆F can be estimated from experiments or simulations, via fluctuation theorems developed in statistical mechanics. Calculating the error in a (∆F )-estimate is difficult. Worse, atypical trials dominate estimates. How many trials one should perform was estimated roughly in [1]. We enhance the approximation with information-theoretic strategies: We quantify “dominance” with a tolerance parameter chosen by the experimenter or simulator. We bound the number of trials one should expect to perform, using the order-∞ Rényi entropy. The bound can be estimated if one implements the “good practice” of bidirectionality, known to improve estimates of ∆F . Estimating ∆F from this number of trials leads to an error that we bound approximately. Numerical experiments on a weakly interacting dilute classical gas support our analytical calculations.