Kim Seongjin, Kim Yong Woon, Talkner Peter, Yi Juyeon
Graduate School of Nanoscience and Technology, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Oct;86(4 Pt 1):041130. doi: 10.1103/PhysRevE.86.041130. Epub 2012 Oct 17.
The estimate of free energy changes based on Bennett's acceptance ratio method is examined in several limiting cases and compared with other estimates based on the Jarzynski equality and on the Crooks relation. While the absolute amount of the dissipated work, defined as the surplus of the average work over the free energy difference, limits the practical applicability of Jarzynski's and Crooks' methods, the reliability of Bennett's approach is restricted by the difference of the dissipated works in the forward and the backward processes. We illustrate these points by considering a Gaussian chain and a hairpin chain which both are extended during the forward and accordingly compressed during the backward protocols. The reliability of the Crooks relation predominantly depends on the sample size; for the Jarzynski estimator the slowness of the work protocol is crucial, and the Bennett method is shown to give precise estimates irrespective of the pulling speed and sample size as long as the dissipated works are the same for the forward and the backward processes as it is the case for Gaussian work distributions. With an increasing dissipated work difference the Bennett estimator also acquires a bias which increases roughly in proportion to this difference. A substantial simplification of the Bennett estimator is provided by the 1/2 formula which expresses the free energy difference by the algebraic average of the Jarzynski estimates for the forward and the backward processes. It agrees with the Bennett estimate in all cases when the Jarzynski and the Crooks estimates fail to give reliable results.
基于贝内特接受率方法的自由能变化估计在几种极限情况下进行了检验，并与基于雅尔津斯基等式和克鲁克斯关系的其他估计进行了比较。虽然定义为平均功超过自由能差的剩余部分的耗散功的绝对量限制了雅尔津斯基方法和克鲁克斯方法的实际适用性，但贝内特方法的可靠性受到正向和反向过程中耗散功差异的限制。我们通过考虑高斯链和发夹链来说明这些要点，这两种链在正向过程中都会伸展，因此在反向协议中会被压缩。克鲁克斯关系的可靠性主要取决于样本大小；对于雅尔津斯基估计器，功协议的缓慢程度至关重要，并且只要正向和反向过程中的耗散功相同（高斯功分布就是这种情况），贝内特方法就被证明无论拉动速度和样本大小如何都能给出精确估计。随着耗散功差异的增加，贝内特估计器也会产生偏差，该偏差大致与这种差异成比例增加。1/2公式对贝内特估计器进行了大幅简化，该公式通过正向和反向过程的雅尔津斯基估计的代数平均值来表示自由能差。当雅尔津斯基估计和克鲁克斯估计无法给出可靠结果时，它在所有情况下都与贝内特估计一致。
