The Kirkwood closure point process: A solution of the Kirkwood-Salsburg equations for negative activities

[2506.08242] The Kirkwood closure point process: A solution of the Kirkwood-Salsburg equations for negative activities Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematical Physics arXiv:2506.08242 (math-ph) [Submitted on 9 Jun 2025 ( v1 ), last revised 9 Apr 2026 (this version, v5)] Title: The Kirkwood closure point process: A solution of the Kirkwood-Salsburg equations for negative activities Authors: Fabio Frommer View a PDF of the paper titled The Kirkwood closure point process: A solution of the Kirkwood-Salsburg equations for negative activities, by Fabio Frommer View PDF HTML (experimental) Abstract: The Kirkwood superposition is a well-known tool in statistical physics to approximate the $n$-point correlation functions for $n\geq 3$ in terms of the density $\rho $ and the radial distribution function $g$ of the underlying system. However, it is unclear whether these approximations are themselves the correlation functions of some point process. If they are, this process is called the Kirkwood closure process. For the case that $g$ is the negative exponential of some nonnegative and regular pair potential $u$ existence of the the Kirkwood closure process was proved by Ambartzumian and Sukiasian. This result was generalized to the case that $u$ is a locally stable and regular pair potential by Kuna, Lebowitz and Speer, provided that $\rho$ is sufficiently small. In this work, it is shown that it suffices for $u$ to be stable and regular to ensure the existence of the Kirkwood closure process. Furthermore, for locally stable $u$ it is proved that the Kirkwood closure process is Gibbs and that the kernel of the GNZ-equation satisfies a Kirkwood-Salsburg type equation. Subjects: Mathematical Physics (math-ph) ; Probability (math.PR) Cite as: arXiv:2506.08242 [math-ph] (or arXiv:2506.08242v5 [math-ph] for this version) https://doi.org/10.48550/arXiv.2506.08242 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Fabio Frommer [ view email ] [v1] Mon, 9 Jun 2025 21:20:42 UTC (26 KB) [v2] Wed, 11 Jun 2025 11:20:09 UTC (26 KB) [v3] Tue, 14 Oct 2025 09:27:15 UTC (27 KB) [v4] Sun, 22 Mar 2026 08:19:25 UTC (33 KB) [v5] Thu, 9 Apr 2026 11:46:10 UTC (34 KB) Full-text links: Access Paper: View a PDF of the paper titled The Kirkwood closure point process: A solution of the Kirkwood-Salsburg equations for negative activities, by Fabio Frommer View PDF HTML (experimental) TeX Source view license Current browse context: math-ph < prev | next > new | recent | 2025-06 Change to browse by: math math.MP math.PR References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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