论文标题
自由能计算的最大核与所有核分布之间的一般关系
A general relation between the largest nucleus and all nuclei distributions for free energy calculations
论文作者
论文摘要
一阶相变的成核率的预测需要了解与自由能型$ W $相关的屏障。分子模拟提供了$ W = -kt \ ln p_a $的直接路线，其中$ k $是Boltzmann的常数，$ t $是温度，而$ p_a $的任何核大小的概率分布。但是实际上，大核的极度稀缺自发发生阻碍了$ p_a $的全面确定，并且必须引入数值偏见，例如关于系统中最大核的大小，导致最大核$ p_l $的概率分布。尽管已知$ p_l $取决于系统大小，但与$ p_a $不同，但它已被广泛用作$ p_a $的近似值。本文提出了$ p_a $和$ p_l $之间的确切关系，该关系可以治愈此近似值，并允许从偏置模拟中准确计算自由能屏障。
Prediction of nucleation rates in first order phase transitions requires the knowledge of the barrier associated to the free energy profile $W$. Molecular simulations offer a direct route through $W = -kT \ln p_a$, where $k$ is Boltzmann's constant, $T$ is temperature, and $p_a$ the probability distribution of the size of any nucleus. But in practice, the extremely scarce spontaneous occurrence of large nuclei impedes the full determination of $p_a$, and a numerical bias must be introduced, e.g. on the size of the largest nucleus in the system, leading to the probability size distribution of the largest nucleus $p_l$. Although $p_l$ is known to be system size dependent, unlike $p_a$, it has been extensively used as an approximation for $p_a$. This paper proposes an exact relation between $p_a$ and $p_l$, which cures this approximation and allows an exact calculation of free energy barriers from biased simulations.
