Abstract Partial molar properties are of fundamental importance for understanding properties of non-ideal mixtures. Josephson and co-workers (Mol. Phys. 2019, 117, 3589–3602) used least squares multiple linear regression to obtain partial molar properties in open constant-pressure ensembles. Assuming composition-independent partial molar properties for the narrow composition range encountered throughout simulation trajectories, we rigorously prove the equivalence of two approaches for computing thermodynamic derivatives in open ensembles of an n-component system: (1) multiple linear regression, and (2) thermodynamic fluctuations. Multiple linear regression provides a conceptually simple and computationally efficient way of computing thermodynamic derivatives for multicomponent systems. We show that in the reaction ensemble, the reaction enthalpy can be computed directly by simple multiple linear regression of the enthalpy as a function of the number of reactant molecules. Non-linear regression and a Gaussian process model taking into account the compositional dependence of partial molar properties further support that multiple linear regression captures the correct physics.

中文翻译：

---

多元线性回归和热力学波动等效于从分子模拟计算热力学导数

摘要 偏摩尔性质对于理解非理想混合物的性质至关重要。Josephson 及其同事 (Mol. Phys. 2019, 117, 3589–3602) 使用最小二乘多元线性回归来获得开放恒压集合中的偏摩尔特性。假设在整个模拟轨迹中遇到的窄组成范围的偏摩尔性质与组成无关，我们严格证明了在 n 分量系统的开放系综中计算热力学导数的两种方法的等效性：（1）多元线性回归，以及（2）热力学波动。多元线性回归提供了一种概念上简单且计算效率高的方法来计算多组分系统的热力学导数。我们证明，在反应系综中，反应焓可以通过作为反应物分子数的函数的焓的简单多元线性回归直接计算。非线性回归和高斯过程模型考虑了偏摩尔特性的组成依赖性，进一步支持多元线性回归捕获正确的物理。