Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions
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. In conclusion, 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.
- Authors:
-
[2];
[3]
- Univ. of North Carolina, Asheville, NC (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Univ. of Tennessee, Knoxville, TN (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1771872
- Grant/Contract Number:
- AC05-00OR22725
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Entropy
- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 2; Journal ID: ISSN 1099-4300
- Publisher:
- MDPI
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; entropy; free energy; entropy functional; pair correlation function; pair distribution function
Citation Formats
Nicholson, Donald M., Gao, C. Y., McDonnell, Marshall T., Sluss, Clifton C., and Keffer, David J. Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions. United States: N. p., 2021.
Web. doi:10.3390/e23020234.
Nicholson, Donald M., Gao, C. Y., McDonnell, Marshall T., Sluss, Clifton C., & Keffer, David J. Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions. United States. https://doi.org/10.3390/e23020234
Nicholson, Donald M., Gao, C. Y., McDonnell, Marshall T., Sluss, Clifton C., and Keffer, David J. Wed .
"Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions". United States. https://doi.org/10.3390/e23020234. https://www.osti.gov/servlets/purl/1771872.
@article{osti_1771872,
title = {Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions},
author = {Nicholson, Donald M. and Gao, C. Y. and McDonnell, Marshall T. and Sluss, Clifton C. and Keffer, David J.},
abstractNote = {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. In conclusion, 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.},
doi = {10.3390/e23020234},
journal = {Entropy},
number = 2,
volume = 23,
place = {United States},
year = {Wed Feb 17 00:00:00 EST 2021},
month = {Wed Feb 17 00:00:00 EST 2021}
}
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