Entropy pair functional theory: Direct entropy evaluation spanning phase transitions

Donald M. Nicholson, C. Y. Gao, Marshall T. McDonnell, Clifton C. Sluss, David J. Keffer

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We prove that, within the class of pair potential Hamiltonians, the excess entropy is a universal, temperature-independent functional of the density and pair correlation function. This result extends Henderson's theorem, which states that the free energy is a temperature dependent functional of the density and pair correlation. The stationarity and concavity of the excess entropy functional are discussed and related to the Gibbs-Bugoliubov inequality and to the free energy. We apply the Kirkwood approximation, which is commonly used for fluids, to both fluids and solids. Approximate excess entropy functionals are developed and compared to results from thermodynamic integration. The pair functional approach gives the absolute entropy and free energy based on simulation output at a single temperature without thermodynamic integration. We argue that a functional of the type, which is strictly applicable to pair potentials, is also suitable for first principles calculation of free energies from Born-Oppenheimer molecular dynamics performed at a single temperature. This advancement has the potential to reduce the evaluation the free energy to a simple modification to any procedure that evaluates the energy and the pair correlation function.

Original languageEnglish
Article number234
Pages (from-to)1-28
Number of pages28
JournalEntropy
Volume23
Issue number2
DOIs
StatePublished - Feb 2021

Funding

Funding: This work was supported by the U. S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division, Oak Ridge National Lab Laboratory and by Nicholson and SUN L.L.C.

Keywords

  • Entropy
  • Entropy functional
  • Free energy
  • Pair correlation function
  • Pair distribution function

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