On the Accurate Estimation of Free Energies Using the Jarzynski Equality
On the Accurate Estimation of Free Energies Using the Jarzynski Equality
复制标题
DOI：
10.1002/jcc.25754
复制
发表时间：
2019-02-05
影响因子：
3
通讯作者：
Rodriguez, Daniela
中科院分区：
文献类型：
--
作者：
Arrar, Mehrnoosh;Martin Boubeta, Fernando;Rodriguez, Daniela
雅金斯基等式是最广为人知和最受关注的非平衡功定理之一，它将自由能与非平衡跃迁中的外功联系起来。在实践中，无限非平衡转变所需的Boltzmann权重的系综平均被估计为有限样本平均，从而产生所谓的Jarzynski估计，Delta(F)Over Cap(J)。或者，Jarzynski等式的二阶近似虽然很少被引用，但对于高斯分布是精确的，并产生了涨落耗散估计器Delta(F)Over Cap(FD)。这里我们推导出自由能的参数极大似然估计(MLE)。考虑属于高斯族或伽马族的单向功分布的覆盖上限(ML)的增量(F)，并将该估计器与覆盖上限(J)的增量(F)进行比较。我们进一步考虑了属于同一家族的双向功分布，并比较了相应的双向Delta(F)over Cap(ML*)和Bennett Accept Ratio(Delta(F)over Cap(BAR))估计。我们证明，对于高斯单向功分布，盖上(FD)的Delta(F)实际上是自由能的参数极大似然估计，因此是这个统计族最有效的估计器。我们观察到，对于单向分布和双向分布，Delta(F)Over Cap(ML)和Delta(F)over Cap(ML*)分别比Delta(F)over Cap(J)和Delta(F)over Cap(BAR)表现得更好。这些结果表明，基本功分布的表征允许雅金斯基等式的最佳使用。(C)2018年威利期刊公司。
The Jarzynski equality is one of the most widely celebrated and scrutinized nonequilibrium work theorems, relating free energy to the external work performed in nonequilibrium transitions. In practice, the required ensemble average of the Boltzmann weights of infinite nonequilibrium transitions is estimated as a finite sample average, resulting in the so-called Jarzynski estimator, Delta(F) over cap (J). Alternatively, the second-order approximation of the Jarzynski equality, though seldom invoked, is exact for Gaussian distributions and gives rise to the Fluctuation-Dissipation estimator Delta(F) over cap (FD). Here we derive the parametric maximum-likelihood estimator (MLE) of the free energy. Delta(F) over cap (ML) considering unidirectional work distributions belonging to Gaussian or Gamma families, and compare this estimator to Delta(F) over cap (J). We further consider bidirectional work distributions belonging to the same families, and compare the corresponding bidirectional Delta(F) over cap (ML*) to the Bennett acceptance ratio (Delta(F) over cap (BAR)) estimator. We show that, for Gaussian unidirectional work distributions, Delta(F) over cap (FD) is in fact the parametric MLE of the free energy, and as such, the most efficient estimator for this statistical family. We observe that Delta(F) over cap (ML) and Delta(F) over cap (ML*) perform better than Delta(F) over cap (J) and Delta(F) over cap (BAR), for unidirectional and bidirectional distributions, respectively. These results illustrate that the characterization of the underlying work distribution permits an optimal use of the Jarzynski equality. (C) 2018 Wiley Periodicals, Inc.