A Leibniz rule of distributional pairing and hyperforce sum rule
Mathematical Physics
2026-03-03 v1 Soft Condensed Matter
Statistical Mechanics
Functional Analysis
math.MP
Abstract
We reformulate and generalize the equilibrium hyperforce sum rule, a generalization of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy, by employing the Schwartz space and its dual. We show that the hyperforce sum rule for the Euclidean space and the equilibrium BBGKY hierarchy at arbitrary level are derived through the Leibniz rule of the derivative for the pairing of tempered distributions and Schwartz functions. We also apply the Leibniz rule to obtain the hyperforce sum rule for systems with periodic boundary conditions.
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Cite
@article{arxiv.2603.01519,
title = {A Leibniz rule of distributional pairing and hyperforce sum rule},
author = {Takashi Maruyama and Tatsuki Seto and Viktor Zaverkin and Henrik Christiansen},
journal= {arXiv preprint arXiv:2603.01519},
year = {2026}
}
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34 pages