Gutenberg Open Science: A variational framework for the inverse Henderson problem of statistical mechanics

Please use this identifier to cite or link to this item: http://doi.org/10.25358/openscience-8300

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DC Field	Value	Language
dc.contributor.author	Frommer, Fabio	-
dc.contributor.author	Hanke, Martin	-
dc.date.accessioned	2022-12-14T10:58:18Z	-
dc.date.available	2022-12-14T10:58:18Z	-
dc.date.issued	2022	-
dc.identifier.uri	https://openscience.ub.uni-mainz.de/handle/20.500.12030/8316	-
dc.description.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.	en_GB
dc.description.sponsorship	Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 491381577	de
dc.language.iso	eng	de
dc.rights	CC BY	*
dc.rights.uri	https://creativecommons.org/licenses/by/4.0/	*
dc.subject.ddc	510 Mathematik	de_DE
dc.subject.ddc	510 Mathematics	en_GB
dc.title	A variational framework for the inverse Henderson problem of statistical mechanics	en_GB
dc.type	Zeitschriftenaufsatz	de
dc.identifier.doi	http://doi.org/10.25358/openscience-8300	-
jgu.type.dinitype	article	en_GB
jgu.type.version	Published version	de
jgu.type.resource	Text	de
jgu.organisation.department	FB 08 Physik, Mathematik u. Informatik	de
jgu.organisation.number	7940	-
jgu.organisation.name	Johannes Gutenberg-Universität Mainz	-
jgu.rights.accessrights	openAccess	-
jgu.journal.title	Letters in mathematical physics	de
jgu.journal.volume	112	de
jgu.pages.alternative	71	de
jgu.publisher.year	2022	-
jgu.publisher.name	Springer Science + Business Media B.V	de
jgu.publisher.place	Dordrecht u.a.	de
jgu.publisher.issn	1573-0530	de
jgu.organisation.place	Mainz	-
jgu.subject.ddccode	510	de
jgu.publisher.doi	10.1007/s11005-022-01563-w	de
jgu.organisation.ror	https://ror.org/023b0x485	-
jgu.subject.dfg	Naturwissenschaften	de
Appears in collections:	DFG-491381577-H

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