{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T13:14:51Z","timestamp":1790082891284,"version":"4.0.1"},"reference-count":58,"publisher":"AIP Publishing","issue":"12","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,9,28]]},"abstract":"<jats:p>Exact theories of electrolyte structure must satisfy the nonlocal constraints imposed by electrostatic screening, yet these constraints are most commonly formulated only for homogeneous bulk systems and at the level of two-point correlations. Here, we develop a unified field-theoretic framework that extends them to general inhomogeneous ionic fluids and nonlinear charge correlations. Using a standard Hubbard\u2013Stratonovich representation of the partition function, we derive an exact Ward identity relating charge-density correlations to the full electrostatic-field propagator. In homogeneous conducting electrolytes, its long-wavelength limit recovers the classical Stillinger\u2013Lovett screening conditions, whereas in inhomogeneous systems, it remains an exact local kernel relation. Repeated functional differentiation generates a nonlinear Ward hierarchy that constrains higher-order charge correlations. We show explicitly how these exact relations are represented in classical density functional theory, Ornstein\u2013Zernike formulations, the random-phase approximation, and the mean-spherical approximation. The resulting hierarchy provides a common bridge between field-theoretic and liquid-state descriptions of electrolytes and supplies rigorous, model-independent consistency tests for approximate theories of screening, response, and correlations in spatially inhomogeneous classical Coulomb fluids.<\/jats:p>","DOI":"10.1063\/5.0351950","type":"journal-article","created":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T12:50:11Z","timestamp":1790081411000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Exact screening constraints for theories of inhomogeneous electrolytes: Generalized Stillinger\u2013Lovett relations and a nonlinear Ward hierarchy"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9061-2745","authenticated-orcid":false,"given":"Yury A.","family":"Budkov","sequence":"first","affiliation":[{"name":"Laboratory of Computational Physics and School of Applied Mathematics, HSE University, Tallinskaya st. 34, 123458 Moscow, Russia and Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, 31-4 Leninsky Prospect, 119071 Moscow, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,22]]},"reference":[{"key":"2026092208500649400_c1","doi-asserted-by":"publisher","first-page":"3858","DOI":"10.1063\/1.1669709","article-title":"Ion-pair theory of concentrated electrolytes. 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