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Hypernetted-chain equation — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Hypernetted-chain_equation
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T13:45:06.687Z
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Hypernetted-chain equation — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Hypernetted-chain_equation (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_b341e8b50d78 (Metraipolis archive dc_b341e8b50d78, sha256 90f3d32bddf98efa28e19d5301d4d1603c51f62f05d056ec43b42d0d7f4f264e)

BibTeX

@misc{dcb341e8b50d78,
  title = {Hypernetted-chain equation — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Hypernetted-chain_equation},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_b341e8b50d78; sha256 90f3d32bddf98efa28e19d5301d4d1603c51f62f05d056ec43b42d0d7f4f264e},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Hypernetted-chain_equation. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In statistical mechanics the hypernetted-chain equation is a closure relation to solve the Ornstein–Zernike equation which relates the direct correlation function to the total correlation function. It is commonly used in fluid theory to obtain e.g. expressions for the radial distribution function. It is given by: ln y ( r 12 ) = ln g ( r 12 ) + β u ( r 12 ) = ρ ∫ [ h ( r 13 ) − ln g ( r 13 ) − β u ( r 13 ) ] h ( r 23 ) d r 3 , {\displaystyle \ln y(r_{12})=\ln g(r_{12})+\beta u(r_{12})=\rho \int \left[h(r_{13})-\ln g(r_{13})-\beta u(r_{13})\right]h(r_{23})\,d\mathbf {r_{3}} ,\,} where ρ = N V {\displaystyle \rho ={\frac {N}{V}}} is the number density of molecules, h ( r ) = g ( r ) − 1 {\displaystyle h(r)=g(r)-1} , g ( r ) {\displaystyle g(r)} is the radial distribution function, u ( r ) {\displaystyle u(r)} is the direct interaction between pairs. β = 1 k B T {\displaystyle \beta ={\frac {1}{k_{\rm {B}}T}}} with T {\displaystyle T} being the Thermodynamic temperature and k B {\displaystyle k_{\rm {B}}} the Boltzmann constant.

Tema degli esploratori: fisica e astronomia (deposito sistematico; categoria «Statistical mechanics»).
Fonte: Wikipedia in inglese, voce «Hypernetted-chain equation» — https://en.wikipedia.org/wiki/Hypernetted-chain_equation
Wikidata Q5958347: «closure relation to solve the Ornstein-Zernike equation» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q5958347
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Hypernetted-chain_equation?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1213449326, consultata il 2026-10-07T13:18:00.079Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 7c88680f1573a7983c4e99eb4e0d08eb9d26bb96f04f86c507c81a336456b18e