{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T20:56:56Z","timestamp":1789160216919,"version":"build-2803163510"},"reference-count":31,"publisher":"AIP Publishing","issue":"10","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,10,1]]},"abstract":"<jats:p>The standard Theory of Critical Phenomena within Boltzmann\u2013Gibbs statistical mechanics is known to successfully predict, at any temperature differing from a continuous-phase-transition critical one, the (finite) values for thermodynamically relevant quantities such as isothermal magnetic susceptibility, specific heat, correlation length, Gr\u00fcneisen parameter, and similar ones. However, at the precise critical point, empirically unreachable infinities emerge within that approach at the N\u2192\u221e thermodynamical limit. Such divergences, although mathematically correct, may be seen as poorly informative ones. Indeed, they make no distinction at all between say the Ising, XY, Heisenberg, and other models. Moreover, for say the XY model, they make no distinction whether the spins are, for instance, 1\/2, 1 or 3\/2, or whether the interactions are say first-neighbor or first-and-second-neighbor ones. The introduction of nonadditive entropic functionals within a consistently generalized statistical mechanics substantially improves the situation, i.e., it regularizes the theory providing informative finite values instead of mere infinities. This undoubtedly enriching fact is illustrated [Soares et al., Phys. Rev. B 111, L060409 (2025)] for the Gr\u00fcneisen parameter at the zero-temperature quantum critical point of a spin-1\/2 ferromagnetic Ising chain in the presence of a transverse magnetic field, by introducing the nonadditive entropic functional Sq with the unique value q=q\u22c6\u226137\u22126=0.0828\u2026, which precisely guarantees the thermodynamical extensivity of the entropy as mandated by the preservation of the Legendre-transform structure of classical thermodynamics.<\/jats:p>","DOI":"10.1063\/5.0290907","type":"journal-article","created":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T12:54:30Z","timestamp":1761051270000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["On the mathematical divergences emerging in the theory of critical phenomena within Boltzmann\u2013Gibbs statistical mechanics"],"prefix":"10.1063","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9387-9194","authenticated-orcid":false,"given":"Constantino","family":"Tsallis","sequence":"first","affiliation":[{"name":"Centro Brasileiro de Pesquisas F\u00edsicas and National Institute of Science and Technology for Complex Systems , Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, ; , 1399 Hyde Park Road, Santa Fe, New Mexico 87501, ; and , Metternichgasse 8, 1030 Vienna,","place":["Brazil USA Austria"]},{"name":"Santa Fe Institute , Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, ; , 1399 Hyde Park Road, Santa Fe, New Mexico 87501, ; and , Metternichgasse 8, 1030 Vienna,","place":["Brazil USA Austria"]},{"name":"Complexity Science Hub Vienna , Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, ; , 1399 Hyde Park Road, Santa Fe, New Mexico 87501, ; and , Metternichgasse 8, 1030 Vienna,","place":["Brazil USA Austria"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2025,10,21]]},"reference":[{"key":"2025102108542421700_c1","first-page":"275","volume":"66","year":"1872","journal-title":"Sitz. 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