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A note on the uniqueness result for the inverse Henderson problem. (English) Zbl 1422.82018

Summary: 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.
©2019 American Institute of Physics

MSC:

82C22 Interacting particle systems in time-dependent statistical mechanics
35R30 Inverse problems for PDEs
62H20 Measures of association (correlation, canonical correlation, etc.)
65C20 Probabilistic models, generic numerical methods in probability and statistics
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