{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:11:09Z","timestamp":1760130669233,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,14]],"date-time":"2023-08-14T00:00:00Z","timestamp":1691971200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FONDECYT","award":["1181558"],"award-info":[{"award-number":["1181558"]}]},{"name":"CONICET (Argentine Agency)","award":["1181558"],"award-info":[{"award-number":["1181558"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We consider an N fermion system at low temperature T in which we encounter special particle number values Nm exhibiting special traits. These values arise when focusing attention upon the degree of mixture (DM) of the pertinent quantum states. Given the coupling constant of the Hamiltonian, the DMs stay constant for all N-values but experience sudden jumps at the Nm. For a quantum state described by the matrix \u03c1, its purity is expressed by Tr\u03c12 and then the degree of mixture is given by 1\u2212Tr\u03c12, a quantity that coincides with the entropy Sq for q=2. Thus, Tsallis entropy of index two faithfully represents the degree of mixing of a state, that is, it measures the extent to which the state departs from maximal purity. Macroscopic manifestations of the degree of mixing can be observed through various physical quantities. Our present study is closely related to properties of many-fermion systems that are usually manipulated at zero temperature. Here, we wish to study the subject at finite temperature. The Gibbs ensemble is appealed to. Some interesting insights are thereby gained.<\/jats:p>","DOI":"10.3390\/e25081206","type":"journal-article","created":{"date-parts":[[2023,8,14]],"date-time":"2023-08-14T10:13:57Z","timestamp":1692008037000},"page":"1206","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Magic Numbers and Mixing Degree in Many-Fermion Systems"],"prefix":"10.3390","volume":"25","author":[{"given":"D.","family":"Monteoliva","sequence":"first","affiliation":[{"name":"UNLP-Comisi\u00f3n de Investigaciones Cient\u00edficas Provincia de Buenos Aires La Plata, La Plata 1900, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5934-2783","authenticated-orcid":false,"given":"A.","family":"Plastino","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica La Plata\u2014CCT-CONICET, Universidad Nacional de La Plata, La Plata 1900, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. R.","family":"Plastino","sequence":"additional","affiliation":[{"name":"CeBio-Departamento de Ciencias B\u00e1sicas, Universidad Nacional del Noroeste, Prov. de Buenos Aires (UNNOBA), CONICET, Junin 6000, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF01016429","article-title":"Possible generalization of Boltzmann-Gibbs statistics","volume":"52","author":"Tsallis","year":"1988","journal-title":"J. Stat. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Gell-Mann, M., and Tsallis, C. (2004). Nonextensive Entropy: Interdisciplinary Applications, Oxford University Press.","DOI":"10.1093\/oso\/9780195159769.001.0001"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"264","DOI":"10.3390\/encyclopedia2010018","article-title":"Entropy","volume":"2","author":"Tsallis","year":"2022","journal-title":"Encyclopedia"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1765","DOI":"10.3390\/e13101765","article-title":"The nonadditive entropy Sq and its applications in physics and elsewhere: Some remarks","volume":"13","author":"Tsallis","year":"2011","journal-title":"Entropy"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Tsallis, C. (2019). Beyond Boltzmann-Gibbs-Shannon in physics and elsewhere. Entropy, 21.","DOI":"10.3390\/e21070696"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"S\u00e1nchez Almeida, J. (2022). The principle of maximum entropy and the distribution of mass in galaxies. Universe, 8.","DOI":"10.3390\/universe8040214"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Tsallis, C. (2023). Introduction to Nonextensive Statistical Mechanics\u2014Approaching a Complex World, Springer. [2nd ed.].","DOI":"10.1007\/978-3-030-79569-6"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/0375-9601(96)00384-2","article-title":"On the generalized Bose-Einstein condensation","volume":"218","author":"Curilef","year":"1996","journal-title":"Phys. Lett. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/S0375-9601(98)00378-8","article-title":"Some bounds upon the nonextensivity parameter using the approximate generalized distribution functions","volume":"245","author":"Tirnakli","year":"1998","journal-title":"Phys. Lett. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/S0375-9601(01)00587-4","article-title":"Generalized statistics and high\u2014Tc superconductivity","volume":"289","author":"Uys","year":"2001","journal-title":"Phys. Lett. A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"054010","DOI":"10.1103\/PhysRevD.78.054010","article-title":"Color superconductivity and Tsallis statistics","volume":"78","author":"Conroy","year":"2008","journal-title":"Phys. Rev. D"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"10004","DOI":"10.1209\/0295-5075\/89\/10004","article-title":"Nonextensive quantum H-theorem","volume":"89","author":"Silva","year":"2010","journal-title":"Europhys. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1016\/j.physa.2015.01.072","article-title":"Non-extensive quantum statistics with particle-hole symmetry","volume":"428","author":"Biro","year":"2015","journal-title":"Phys. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"455","DOI":"10.3390\/physics2030026","article-title":"Fractal Structures of Yang-Mills Fields and Non-Extensive Statistics: Applications to High Energy Physics","volume":"2","author":"Deppman","year":"2020","journal-title":"Physics"},{"key":"ref_15","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_16","unstructured":"Jaeger, G. (2007). Qantum Information: An Overview, Springer."},{"key":"ref_17","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_18","first-page":"5","article-title":"Analytical and numerical analysis of the complete Lipkin\u2013Meshkov\u2013Glick Hamiltonian","volume":"27","year":"2018","journal-title":"Int. J. Mod. Phys. E"},{"key":"ref_19","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_20","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/0370-2693(81)90001-0","article-title":"Surprisal Approach to Cold Fission Processes","volume":"98","author":"Otero","year":"1981","journal-title":"Phys. Lett. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3599","DOI":"10.1103\/PhysRevLett.81.3599","article-title":"Odd-Even Staggering of Nuclear Masses: Pairing or Shape Effect?","volume":"81","author":"Dobaczewski","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"014311","DOI":"10.1103\/PhysRevC.65.014311","article-title":"Pairing correlations. II. Microscopic analysis of odd-even mass staggering in nuclei","volume":"65","author":"Dugett","year":"2001","journal-title":"Phys. Rev. C"},{"key":"ref_23","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_24","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1140\/epja\/i2005-10133-0","article-title":"Landau-Ginzburg method applied to finite fermion systems: Pairing in nuclei","volume":"25","author":"Kruse","year":"2005","journal-title":"Eur. J. Phys. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1016\/S0378-4371(02)01348-1","article-title":"Multiple phases in a new statistical boson fermion model of superconductivity","volume":"317","author":"Tolmachev","year":"2003","journal-title":"Phys. A"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"051301","DOI":"10.1103\/PhysRevC.60.051301","article-title":"Mean-field and blocking effects on odd-even mass differences and rotational motion of nuclei","volume":"60","author":"Xu","year":"1999","journal-title":"Phys. Rev. C"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1034","DOI":"10.1103\/PhysRevLett.78.1034","article-title":"Universal Shapes of Small Fermion Clusters","volume":"78","author":"Kolehmainen","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_28","first-page":"237","article-title":"Electron Correlations in Narrow Energy Bands","volume":"276","author":"Hubbard","year":"1963","journal-title":"Proc. R. Soc. Lond."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"5866","DOI":"10.1016\/j.amc.2010.12.072","article-title":"Exact solutions to nonlinear Schrodinger equation with variable coefficients","volume":"217","author":"Liu","year":"2011","journal-title":"Appl. Math. Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"123030","DOI":"10.1088\/1367-2630\/15\/12\/123030","article-title":"Quantum criticality and population trapping of fermions by non-equilibrium lattice modulations","volume":"15","author":"Frank","year":"2013","journal-title":"New J. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1140\/epjb\/e2019-100087-0","article-title":"Evolution of Floquet topological quantum states in driven semiconductors","volume":"92","author":"Lubatsch","year":"2019","journal-title":"Eur. Phys. J. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1244","DOI":"10.1103\/PhysRevC.26.1244","article-title":"Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes","volume":"26","author":"Feng","year":"1992","journal-title":"Phys. Rev. C"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/0375-9474(81)90117-2","article-title":"Maximum Overlap, Atomic Coherent States and the Generator Coordinate Method","volume":"356","author":"Bozzolo","year":"1981","journal-title":"Nucl. Phys. A"},{"key":"ref_34","first-page":"127","article-title":"Statistical Quantifiers Resolve a Nuclear Theory Controversy","volume":"4","author":"Monteoliva","year":"2022","journal-title":"Q. Rep."},{"key":"ref_35","unstructured":"Reif, F. (1965). Fundamentals of Statistical Theoretic and Thermal Physics, McGraw Hill."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1927","DOI":"10.1016\/j.physleta.2010.02.040","article-title":"Thermal effects in quantum phase-space distributions","volume":"37","author":"Pennini","year":"2010","journal-title":"Phys. Lett. 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