Entropy functional universality: Correlation, response, many-body interaction, multi-component, quantum, hyperfunctional, and Ornstein-Zernike structure
Abstract
We give a comprehensive account of the recent entropy functional theory for the equilibrium statistical mechanics of classical many-body systems (arXiv:2606.28240). The approach is formally exact and based on a joint grand potential minimization principle for the one-body density and the global pair distance distribution. These variational fields depend respectively on position and on scalar distance, which retains the low computational complexity of standard density functional theory. Correlation effects are contained in a unique excess entropy functional, which is universal across all systems with pairwise interparticle potentials. Functional differentiation yields entropic direct correlation functionals that generate entropic response and fluctuation correlation functions via coupled Ornstein-Zernike equations. Two alternative proofs are given for the existence and uniqueness of the underlying metadensity functional map, based on generalizations of either Levy's constrained search method or Mermin-Evans proof by contradiction. Simple excess entropy approximations yield the standard mean-field and second-virial excess free energy density functionals. We describe exact entropic functional line integrals, make connections to the recent one-body fluctuation profiles, and generalize the entropy approach beyond pairwise interparticle potentials via parametric dependence or reduction operators. We also lay out the formulation for multi-component systems, the hyperfunctional for general observables, and the quantum entropy functional.
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BibTeX
@misc{schmidt2026entropy,
title = {{Entropy functional universality: Correlation, response, many-body interaction, multi-component, quantum, hyperfunctional, and Ornstein-Zernike structure}},
author = {Matthias Schmidt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.03032},
eprint = {2607.03032},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.03032},
}
RIS
TY - UNPB
TI - Entropy functional universality: Correlation, response, many-body interaction, multi-component, quantum, hyperfunctional, and Ornstein-Zernike structure
AU - Matthias Schmidt
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2607.03032
UR - https://arxiv.org/abs/2607.03032
AB - We give a comprehensive account of the recent entropy functional theory for the equilibrium statistical mechanics of classical many-body systems (arXiv:2606.28240). The approach is formally exact and based on a joint grand potential minimization principle for the one-body density and the global pair distance distribution. These variational fields depend respectively on position and on scalar distance, which retains the low computational complexity of standard density functional theory. Correlation effects are contained in a unique excess entropy functional, which is universal across all systems with pairwise interparticle potentials. Functional differentiation yields entropic direct correlation functionals that generate entropic response and fluctuation correlation functions via coupled Ornstein-Zernike equations. Two alternative proofs are given for the existence and uniqueness of the underlying metadensity functional map, based on generalizations of either Levy's constrained search method or Mermin-Evans proof by contradiction. Simple excess entropy approximations yield the standard mean-field and second-virial excess free energy density functionals. We describe exact entropic functional line integrals, make connections to the recent one-body fluctuation profiles, and generalize the entropy approach beyond pairwise interparticle potentials via parametric dependence or reduction operators. We also lay out the formulation for multi-component systems, the hyperfunctional for general observables, and the quantum entropy functional.
ER -