Letters in Mathematical Physics

, Volume 108, Issue 2, pp 285–306 | Cite as

Fréchet differentiability of molecular distribution functions I. \(L^\infty \) analysis

  • Martin HankeEmail author


For a grand canonical ensemble of classical point-like particles at equilibrium in continuous space, we investigate the functional relationship between a stable and regular pair potential describing the interaction of the particles and the corresponding molecular distribution functions. For certain admissible perturbations of the pair potential and sufficiently small activity, we rigorously establish Frechet differentiability with respect to the supremum norm in the image space—both for bounded domains and in the thermodynamical limit.


Statistical mechanics Molecular distribution function Fréchet derivative Kirkwood–Salsburg equations 

Mathematics Subject Classification

82B21 82B80 


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Institut für MathematikJohannes Gutenberg-Universität MainzMainzGermany

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