Wu Di, Kofke David A
Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA.
J Chem Phys. 2004 Nov 8;121(18):8742-7. doi: 10.1063/1.1806413.
We present a model for the bias of free-energy differences when determined using the nonequilibrium work (NEW) formalism due to Jarzynski. Input to the model is the distribution of work values underlying the NEW calculation, and the bias is estimated by assuming that all of the inaccuracy is incurred by failure to sample work values beyond a specific point in the tail of the distribution. The model is formulated considering both small- and large-sample NEW calculations. It is then applied to the study of bias for cases in which the work distribution is Gaussian. The model is shown to give an excellent description of the bias in situations where the bias is a more significant source of error than the sample variance. A scaling law is presented and it is shown that the bias as a function of sampling can be reduced to a single universal curve, approximately valid for all Gaussian work distributions. This result is used to formulate a simple criterion that can be applied to test if a NEW calculation is effectively free of bias. The criterion is shown to be effective even though it uses the measured (and perhaps biased) free energy as an input.
我们提出了一个模型，用于研究在使用由雅尔津斯基提出的非平衡功（NEW）形式主义确定自由能差时的偏差。该模型的输入是NEW计算所基于的功值分布，通过假设所有不准确性都是由于未能对分布尾部超出特定点的功值进行采样而产生的，来估计偏差。该模型在考虑小样本和大样本NEW计算的情况下构建而成。然后将其应用于研究功分布为高斯分布的情况下的偏差。结果表明，在偏差比样本方差更显著地成为误差来源的情况下，该模型能很好地描述偏差。我们提出了一个标度律，并表明偏差作为采样的函数可以简化为一条单一的通用曲线，该曲线对所有高斯功分布大致有效。这一结果被用于制定一个简单的准则，可用于检验NEW计算是否实际上无偏差。结果表明，即使该准则使用测量得到的（可能有偏差的）自由能作为输入，它也是有效的。
