Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions
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Department of Physics and Astronomy, University of North Carolina, Asheville, NC 28803, USA
2
Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
3
Department of Materials Science and Engineering, University of Tennessee, Knoxville, Knoxville, TN 37996, USA
*
Author to whom correspondence should be addressed.
Academic Editors: Philip Broadbridge and Keivan Esfarjani
Entropy 2021, 23(2), 234; https://doi.org/10.3390/e23020234
Received: 19 December 2020
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Revised: 9 February 2021
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Accepted: 11 February 2021
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Published: 17 February 2021
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.
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Keywords:
entropy; free energy; entropy functional; pair correlation function; pair distribution function
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MDPI and ACS Style
Nicholson, D.M.; Gao, C.Y.; McDonnell, M.T.; Sluss, C.C.; Keffer, D.J. Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions. Entropy 2021, 23, 234. https://doi.org/10.3390/e23020234
AMA Style
Nicholson DM, Gao CY, McDonnell MT, Sluss CC, Keffer DJ. Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions. Entropy. 2021; 23(2):234. https://doi.org/10.3390/e23020234
Chicago/Turabian StyleNicholson, Donald M., C. Y. Gao, Marshall T. McDonnell, Clifton C. Sluss, and David J. Keffer. 2021. "Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions" Entropy 23, no. 2: 234. https://doi.org/10.3390/e23020234
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