Multiple linear regression and thermodynamic fluctuations are equivalent for computing thermodynamic derivatives from molecular simulation

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.