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

Ahmadreza Rahbari, Tyler R. Josephson, Yangzesheng Sun, Othonas A. Moultos, David Dubbeldam, J. Ilja Siepmann, Thijs J.H. Vlugt

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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.

Original languageEnglish (US)
Article number112785
JournalFluid Phase Equilibria
StatePublished - Nov 15 2020

Bibliographical note

Funding Information:
This work was supported by NWO Exacte Wetenschappen (Physical Sciences) for the use of supercomputer facilities, with financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (Netherlands Organization for Scientific Research, NWO). TJHV acknowledges NWO-CW for a VICI grant. This work was also supported by the Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences, under Award DE-FG02-17ER16362 (TJR, YS, and JIS ). Computational resources from the Minnesota Supercomputing Institute are also gratefully acknowledged.

Publisher Copyright:
© 2020 The Author(s)


  • Linear regression
  • Molecular simulation
  • Open ensembles thermodynamic fluctuations
  • Partial molar properties


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