{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T16:14:50Z","timestamp":1791994490399,"version":"4.4.0"},"reference-count":59,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T00:00:00Z","timestamp":1768176000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nanomaterials"],"abstract":"<jats:p>Nanoscopic quantum dots exhibit discrete energy spectra and size- and shape-dependent thermal properties that cannot always be adequately described within the conventional Boltzmann\u2013Gibbs statistical framework. In systems with strong confinement, finite size, and reduced symmetry, deviations from extensivity may emerge, affecting the occupation of energy levels and the resulting thermodynamic response. In this context, this work elucidates how GaAs quantum dot geometry, external electric fields, and nonextensive statistical effects jointly influence the thermal response of quantum dots with different geometries\u2014cubic, cylindrical, ellipsoidal, and pyramidal. These energy levels are calculated by solving the Schr\u00f6dinger equation under the effective mass approximation, employing the finite element method for numerical computation. These energy levels are then incorporated into an iterative numerical procedure to calculate the specific heat for different values of the nonextensivity parameter, thereby enabling exploration of both extensive (Boltzmann\u2013Gibbs) and nonextensive regimes. The results demonstrate that the shape of the quantum dots strongly influences the energy spectrum and, consequently, the thermal properties, producing distinctive features such as Schottky-type anomalies and geometry-dependent shifts under an external electric field. In subextensive regimes, a discrete behavior in the specific heat emerges due to natural cutoffs in the accessible energy states. In contrast, in superextensive regimes, a smooth, saturation-like behavior is observed. These findings highlight the importance of geometry, external-field effects, and nonextensive statistics as complementary tools for tailoring the energy distribution and thermal response in nanoscopic quantum systems.<\/jats:p>","DOI":"10.3390\/nano16020094","type":"journal-article","created":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T10:25:23Z","timestamp":1768213523000},"page":"94","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Nonextensive Statistics in Nanoscopic Quantum Dots"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8666-688X","authenticated-orcid":false,"given":"John A.","family":"Gil-Corrales","sequence":"first","affiliation":[{"name":"Facultad de Ciencias, Instituto Tecnol\u00f3gico Metropolitano (ITM)-Instituci\u00f3n Universitaria, Campus Fraternidad, Calle 73 No. 76A-354 V\u00eda al Volador, Medell\u00edn 050034, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4004-1726","authenticated-orcid":false,"given":"Alvaro L.","family":"Morales","sequence":"additional","affiliation":[{"name":"Grupo de Materia Condensada-UdeA, Instituto de F\u00edsica, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Cl 70 No. 52-21, Medell\u00edn 050010, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3382-2783","authenticated-orcid":false,"given":"Carlos A.","family":"Duque","sequence":"additional","affiliation":[{"name":"Grupo de Materia Condensada-UdeA, Instituto de F\u00edsica, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Cl 70 No. 52-21, Medell\u00edn 050010, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"117500","DOI":"10.1016\/j.optmat.2025.117500","article-title":"Engineering InAs quantum dot pairs: Tailoring structural and optical properties with GaAs and GaAsSb spacer layers","volume":"168","author":"Salhi","year":"2025","journal-title":"Opt. 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