The inverse Henderson problem of statistical mechanics is the theoretical foundation for many bottom-up coarse-graining techniques for the numerical simulation of complex soft matter physics. This inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles. Roughly stated, it asks for the interaction potential given the equilibrium pair correlation function of the system. In 1974, Henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system. Here, we provide a rigorous proof of a slightly more general version of the latter statement using Georgii’s variant of the Gibbs variational principle.
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A note on the uniqueness result for the inverse Henderson problem
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September 2019
Research Article|
September 27 2019
A note on the uniqueness result for the inverse Henderson problem

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F. Frommer
;
F. Frommer
a)
1
Institut für Mathematik, Johannes Gutenberg-Universität Mainz
, 55099 Mainz, Germany
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M. Hanke
;
M. Hanke
b)
1
Institut für Mathematik, Johannes Gutenberg-Universität Mainz
, 55099 Mainz, Germany
Search for other works by this author on:
F. Frommer
1,a)
M. Hanke
1,b)
S. Jansen
2,c)
1
Institut für Mathematik, Johannes Gutenberg-Universität Mainz
, 55099 Mainz, Germany
2
Institut für Mathematik, Ludwig-Maximilians Universität München
, Theresienstr. 39, 80333 München, Germany
J. Math. Phys. 60, 093303 (2019)
Article history
Received:
June 03 2019
Accepted:
September 04 2019
Connected Content
A companion article has been published:
Inverse Henderson problem generalization fills gap for numerical simulations of soft matter
Citation
F. Frommer, M. Hanke, S. Jansen; A note on the uniqueness result for the inverse Henderson problem. J. Math. Phys. 1 September 2019; 60 (9): 093303. https://doi.org/10.1063/1.5112137
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