{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T13:07:10Z","timestamp":1770988030412,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T00:00:00Z","timestamp":1769904000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009232","name":"University of Debrecen","doi-asserted-by":"publisher","award":["0484\/025"],"award-info":[{"award-number":["0484\/025"]}],"id":[{"id":"10.13039\/501100009232","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009232","name":"University of Debrecen","doi-asserted-by":"publisher","award":["PTP\/0484\/2025"],"award-info":[{"award-number":["PTP\/0484\/2025"]}],"id":[{"id":"10.13039\/501100009232","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Junta de Andaluc\\'\\i","award":["FQM420"],"award-info":[{"award-number":["FQM420"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Within density functional theory (DFT), where the density is the fundamental variable, quantum phase transitions (QPTs) can be formulated through a Hamiltonian\u00a0H^=H^0+\u2211i\u03beiA^i, such that the control parameters\u00a0{\u03bei}\u00a0are in bijective correspondence (in the nondegenerate case) with the \u201cdensities\u201d\u00a0ai=\u27e8A^i\u27e9, and the functional\u00a0Q({ai})\u00a0acts as the Legendre transform of the energy; this structure even permits the use of R\u00e9nyi entropy (for a given order) as an alternative control parameter, while degeneracy can be handled via a subspace density. On this foundation, information-theoretic measures provide sensitive diagnostics of criticality: fidelity and its susceptibility\u00a0\u03c7, Fisher information, relative R\u00e9nyi entropy, and the Kullback\u2013Leibler divergence are locally linked by\u00a0Rq\u2248qIKL\u22482q\u03c7(\u03b4\u03bb)2, revealing their proportionality in the small-parameter-shift regime. Applied to the Dicke model, numerical analyses show that fidelity exhibits pronounced curvature or divergence near\u00a0\u03bbc=\u03c9\u03c90\/2\u00a0and that the response sharpens with increasing j, corroborating that these information measures capture QPTs with precision within the DFT framework.<\/jats:p>","DOI":"10.3390\/e28020170","type":"journal-article","created":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T09:48:08Z","timestamp":1770025688000},"page":"170","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Density Functional Theory and Information-Theoretic Diagnostics of Quantum Phase Transitions"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8088-9887","authenticated-orcid":false,"given":"Elvira","family":"Romera","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica At\u00f3mica, Molecular y Nuclear and Instituto Carlos I de F\u00edsica Te\u00f3rica y Computacional, Universidad de Granada, Fuentenueva s\/n, 18071 Granada, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2605-9644","authenticated-orcid":false,"given":"\u00c1gnes","family":"Nagy","sequence":"additional","affiliation":[{"name":"Department of Theoretical Physics, University of Debrecen, H-4002 Debrecen, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. 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