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For non-equilibrium transport properties, this amounts to establishing Green\u2013Kubo (GK) relationships. In hydrodynamics, relating such GK expressions for liquid\u2013solid friction to macroscopic slip boundary conditions has remained a long-standing problem due to two challenges: (i) The GK running integral of the force autocorrelation function decays to zero rather than reaching a well-defined plateau value, and (ii) debates persist on whether such a transport coefficient measures an intrinsic interfacial friction or an effective friction in the system. Inspired by ideas from the coarse-graining community, we derive a GK relation for liquid\u2013solid friction where the force autocorrelation is sampled with a constraint of momentum conservation in the liquid. Our expression does not suffer from the \u201cplateau problem\u201d and unambiguously measures an effective friction coefficient, in an analogous manner to Stokes\u2019 law. We further establish a link between the derived friction coefficient and the hydrodynamic slip length, enabling a straightforward assessment of continuum hydrodynamics across length scales. We find that continuum hydrodynamics describes the simulation results quantitatively for confinement length scales all the way down to 1\u00a0nm. Our approach amounts to a straightforward modification to the present standard method of quantifying interfacial friction from molecular simulations, making possible a sensible comparison between surfaces of vastly different slippage.<\/jats:p>","DOI":"10.1063\/5.0238363","type":"journal-article","created":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T05:41:31Z","timestamp":1732686091000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":14,"title":["Revisiting the Green\u2013Kubo relation for friction in nanofluidics"],"prefix":"10.1063","volume":"161","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0981-4329","authenticated-orcid":false,"given":"Anna T.","family":"Bui","sequence":"first","affiliation":[{"name":"Yusuf Hamied Department of Chemistry, University of Cambridge 1 , Lensfield Road, Cambridge CB2 1EW,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2708-8711","authenticated-orcid":false,"given":"Stephen J.","family":"Cox","sequence":"additional","affiliation":[{"name":"Yusuf Hamied Department of Chemistry, University of Cambridge 1 , Lensfield Road, Cambridge CB2 1EW,","place":["United Kingdom"]},{"name":"Department of Chemistry, Durham University 2 , South Road, Durham DH1 3LE,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2024,11,27]]},"reference":[{"key":"2024112710411075500_c1","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1038\/nature11876","volume":"494","year":"2013","journal-title":"Nature"},{"key":"2024112710411075500_c2","doi-asserted-by":"publisher","first-page":"15249","DOI":"10.1021\/acsnano.1c05931","volume":"15","year":"2021","journal-title":"ACS Nano"},{"key":"2024112710411075500_c3","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1038\/s41563-020-0625-8","volume":"19","year":"2020","journal-title":"Nat. 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