{"paper":{"title":"Shannon and R\\'enyi entropies of molecular densities: insights into extensivity and the incomplete description of electron correlation","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"Electron-density entropies fail to capture static correlation and often violate extensivity.","cross_cats":["physics.chem-ph"],"primary_cat":"quant-ph","authors_text":"\\'Angel Mart\\'in Pend\\'as, Diogo J. L. Rodrigues, Evelio Francisco","submitted_at":"2026-04-20T10:53:35Z","abstract_excerpt":"In this work, we investigate the reliability of information-theoretic measures based on the electron-density and shape-function, specifically Shannon and R\\'enyi entropies, as descriptors of electronic correlation. By establishing a rigorous decomposition of these entropic measures into additive and nonadditive contributions, supported on a Mulliken-like atomic partition of molecules, we systematically analyze the asymptotic behavior of the entropies at the infinite-internuclear-distance limit to assess the problem of static correlation and extensivity. Our algebraic and numerical analysis rev"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"electron-density-based measures are insufficient for capturing static correlation, suggesting that robust entropic descriptors should be constructed from higher-dimensional Hilbert-space objects.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Mulliken-like atomic partition combined with the infinite-separation asymptotic analysis correctly isolates and quantifies static correlation and extensivity properties of the underlying wavefunction.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Shannon and Rényi entropies from molecular electron densities fail to encode static correlation and violate extensivity, indicating density-based descriptors are insufficient.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Electron-density entropies fail to capture static correlation and often violate extensivity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"18313a06274e2cdfa407b8fa5cb6f6fe60649ea2df7fb8db56ba3a28836e3b6f"},"source":{"id":"2604.18081","kind":"arxiv","version":1},"verdict":{"id":"560dea0b-1424-4ff4-a496-271853a53c68","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T05:19:14.166745Z","strongest_claim":"electron-density-based measures are insufficient for capturing static correlation, suggesting that robust entropic descriptors should be constructed from higher-dimensional Hilbert-space objects.","one_line_summary":"Shannon and Rényi entropies from molecular electron densities fail to encode static correlation and violate extensivity, indicating density-based descriptors are insufficient.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Mulliken-like atomic partition combined with the infinite-separation asymptotic analysis correctly isolates and quantifies static correlation and extensivity properties of the underlying wavefunction.","pith_extraction_headline":"Electron-density entropies fail to capture static correlation and often violate extensivity."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.18081/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-20T04:27:42.378119Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"bb93692a979d3249b491993312c8094c1278676475f38613009010e9a9359995"},"references":{"count":109,"sample":[{"doi":"","year":1948,"title":"Shannon, C. E. A mathematical theory of communication.Bell System Tech- nical Journal27, 379–423 (1948)","work_id":"","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"Brillouin, L.Science and information theory(Courier Corporation, 2013)","work_id":"","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2007,"title":"Frieden, B. R., Luo, S. & Plastino, A. Physics and information.Physics Today 60, 14 (2007)","work_id":"","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1957,"title":"Jaynes, E. T. Information theory and statistical mechanics.Physical Review 106, 620–630 (1957)","work_id":"","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2007,"title":"Gatenby, R. A. & Frieden, B. R. Information theory in living systems, meth- ods, applications, and challenges.Bulletin of Mathematical Biology69, 635– 657 (2007)","work_id":"","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":6,"snapshot_sha256":"70192fab5c84f84f4b138dec6089e263dd4ed09067dbf00c76b7838fe8b1b999","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}