Departament de Física Fonamental, Universitat de Barcelona, Spain.
Phys Rev Lett. 2011 Aug 5;107(6):060601. doi: 10.1103/PhysRevLett.107.060601. Epub 2011 Aug 2.
We derive analytical expressions for the bias of the Jarzynski free-energy estimator from N nonequilibrium work measurements, for a generic work distribution. To achieve this, we map the estimator onto the random energy model in a suitable scaling limit parametrized by (logN)/μ, where μ measures the width of the lower tail of the work distribution, and then compute the finite-N corrections to this limit with different approaches for different regimes of (logN)/μ. We show that these expressions describe accurately the bias for a wide class of work distributions and exploit them to build an improved free-energy estimator from unidirectional work measurements. We apply the method to optical tweezers unfolding and refolding experiments on DNA hairpins of varying loop size and dissipation, displaying both near-Gaussian and non-Gaussian work distributions.
我们从 N 个非平衡功测量中推导出了雅可比自由能估计的偏差的解析表达式，适用于一般的功分布。为此，我们将估计器映射到随机能量模型中，在适当的缩放极限中用 (logN)/μ 参数化，其中 μ 度量功分布的下尾宽度，然后用不同的方法计算此极限的有限-N 修正，适用于不同的 (logN)/μ 区域。我们表明，这些表达式准确描述了广泛类别的功分布的偏差，并利用它们从单向功测量中构建改进的自由能估计器。我们将该方法应用于 DNA 发夹的光镊展开和折叠实验，该实验的环大小和耗散各不相同，显示出接近高斯和非高斯的功分布。
