Please use this identifier to cite or link to this item: http://doi.org/10.25358/openscience-8300
Authors: Frommer, Fabio
Hanke, Martin
Title: A variational framework for the inverse Henderson problem of statistical mechanics
Online publication date: 14-Dec-2022
Year of first publication: 2022
Language: english
Abstract: The inverse Henderson problem refers to the determination of the pair potential which specifies the interactions in an ensemble of classical particles in continuous space, given the density and the equilibrium pair correlation function of these particles as data. For a canonical ensemble in a bounded domain, it has been observed that this pair potential minimizes a corresponding convex relative entropy functional, and that the Newton iteration for minimizing this functional coincides with the so-called inverse Monte Carlo (IMC) iterative scheme. In this paper, we show that in the thermodynamic limit analogous connections exist between the specific relative entropy introduced by Georgii and Zessin and a proper formulation of the IMC iteration in the full space. This provides a rigorous variational framework for the inverse Henderson problem, valid within a large class of pair potentials, including, for example, Lennard-Jones-type potentials. It is further shown that the pressure is strictly convex as a function of the pair potential and the chemical potential, and that the specific relative entropy at fixed density is a strictly convex function of the pair potential. At a given reference potential and a corresponding density in the gas phase, we determine the gradient and the Hessian of the specific relative entropy, and we prove that the Hessian extends to a symmetric positive semidefinite quadratic functional in the space of square integrable perturbations of this potential.
DDC: 510 Mathematik
510 Mathematics
Institution: Johannes Gutenberg-Universität Mainz
Department: FB 08 Physik, Mathematik u. Informatik
Place: Mainz
ROR: https://ror.org/023b0x485
DOI: http://doi.org/10.25358/openscience-8300
Version: Published version
Publication type: Zeitschriftenaufsatz
License: CC BY
Information on rights of use: https://creativecommons.org/licenses/by/4.0/
Journal: Letters in mathematical physics
112
Pages or article number: 71
Publisher: Springer Science + Business Media B.V
Publisher place: Dordrecht u.a.
Issue date: 2022
ISSN: 1573-0530
Publisher DOI: 10.1007/s11005-022-01563-w
Appears in collections:DFG-491381577-H

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