{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T16:46:39Z","timestamp":1774543599957,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T00:00:00Z","timestamp":1736121600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"CONICET"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this study, we utilize information theory tools to investigate notable features of the quantum degree of mixedness (Cf) in a finite model of N interacting fermions. This model serves as a simplified proxy for an atomic nucleus, capturing its essential features in a more manageable form compared to a realistic nuclear model, which would require the diagonalization of matrices with millions of elements, making the extraction of qualitative features a significant challenge. Specifically, we aim to correlate Cf with particle number fluctuations and temperature, using the paradigmatic Lipkin model. Our analysis reveals intriguing dependencies of Cf on the total fermion number, showcasing distinct behaviors at different temperatures. Notably, we find that the degree of quantum mixedness exhibits a strong dependence on the total fermion number, with varying trends across different temperature regimes. Remarkably, this dependence remains unaffected by the strength of the fermion\u2013fermion interaction (as long as it is non-zero), underscoring the robustness of the observed phenomena. Through comprehensive numerical simulations, we provide illustrative graphs depicting these dependencies, offering valuable insights into the fundamental characteristics of quantum many-body fermion systems. Our findings illuminate the intricate dynamics of the degree of mixedness, a crucial quantum property, with potential implications for diverse fields ranging from condensed matter physics to quantum information science.<\/jats:p>","DOI":"10.3390\/e27010037","type":"journal-article","created":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T08:08:52Z","timestamp":1736150932000},"page":"37","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Information Theoretical Analysis of Quantum Mixedness in a Finite Model of Interacting Fermions"],"prefix":"10.3390","volume":"27","author":[{"given":"Diana","family":"Monteoliva","sequence":"first","affiliation":[{"name":"UNLP-Comisi\u00f3n de Investigaciones Cient\u00edficas Provincia de Buenos Aires, La Plata 1900, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5934-2783","authenticated-orcid":false,"given":"Angelo","family":"Plastino","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica La Plata, CCT-CONICET, Universidad Nacional de La Plata, La Plata 1900, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angel Ricardo","family":"Plastino","sequence":"additional","affiliation":[{"name":"CeBio-Departamento de Ciencias B\u00e1sicas, Universidad Nacional del Noroeste Provincia de Buenos Aires (UNNOBA), CONICET, Junin 6000, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,6]]},"reference":[{"key":"ref_1","unstructured":"Messiah, A. (1966). Quantum Mechanics, John Wiley."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Cohen-Tannoudji, C., Diu, B., and Lalo\u00eb, F. (2020). Quantum Mechanics, John Wiley.","DOI":"10.1515\/9783110638738"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Peres, A. (1995). Quantum Theory: Concepts and Methods, Kluwer Academic Publishers.","DOI":"10.1119\/1.17946"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Sakurai, J.J., and Napolitano, J. (2020). Modern Quantum Mechanics, Cambridge University Press.","DOI":"10.1017\/9781108587280"},{"key":"ref_5","unstructured":"Dirac, P.A.M. (1981). The Principles of Quantum Mechanics, Oxford University Press."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ring, P., and Schuck, P. (1980). The Nuclear Many-Body Problem, Springer.","DOI":"10.1007\/978-3-642-61852-9"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/0029-5582(65)90862-X","article-title":"Validity of many-body approximation methods for a solvable model: (I). Exact solutions and perturbation theory","volume":"62","author":"Lipkin","year":"1965","journal-title":"Nucl. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0029-5582(65)90862-X","article-title":"Validity of many-body approximation methods for a solvable model: (II) Linearization procedure","volume":"62","author":"Lipkin","year":"1965","journal-title":"Nucl. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Bengtsson, I., and Zyczkowsi, K. (2006). Geometry of Quantum States: An Introduction to Quantum Entanglement, Cambridge University Press.","DOI":"10.1017\/CBO9780511535048"},{"key":"ref_10","unstructured":"Jaeger, G. (2007). Quantum Information: An Overview, Springer."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Giulini, D., Kiefer, C., and Kupsch, J. (1996). Decoherence and the Appearance of a Classical World in Quantum Theory, Springer.","DOI":"10.1007\/978-3-662-03263-3"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"052108","DOI":"10.1103\/PhysRevA.63.052108","article-title":"Decoherence versus entropy in neutron interferometry","volume":"63","author":"Facchi","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Plastino, A.R., Monteoliva, D., and Plastino, A. (2021). Information-theoretic features of many fermion systems: An exploration based on exactly solvable models. Entropy, 23.","DOI":"10.3390\/e23111488"},{"key":"ref_14","first-page":"127","article-title":"Statistical Quantifiers Resolve a Nuclear Theory Controversy","volume":"4","author":"Monteoliva","year":"2022","journal-title":"Q. Rep."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2340","DOI":"10.1103\/PhysRevC.27.2340","article-title":"Comparison of upper and lower bound methods using a soluble many-Fermion model","volume":"27","author":"Cambiaggio","year":"1983","journal-title":"Phys. Rev. C"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/1\/37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:23:34Z","timestamp":1759919014000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/1\/37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,6]]},"references-count":15,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["e27010037"],"URL":"https:\/\/doi.org\/10.3390\/e27010037","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,6]]}}}