Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: New route to nonextensive thermostatistics

dc.contributor.authorJizba, P.
dc.contributor.authorLambiase, G.
dc.contributor.authorLuciano, Giuseppe Gaetano
dc.contributor.authorPetruzziello, L.
dc.date.accessioned2024-06-12T08:50:36Z
dc.date.available2024-06-12T08:50:36Z
dc.date.issued2023
dc.description.abstractWe study coherent states associated with a generalized uncertainty principle (GUP). We separately analyze the cases of positive and negative deformation parameter 𝛽, showing that the ensuing probability distribution is a Tsallis distribution whose nonextensivity parameter π‘ž is monotonically related to 𝛽. Moreover, for 𝛽<0 (corresponding to π‘ž<1), we reformulate the GUP in terms of a one-parameter class of Tsallis entropy-power-based uncertainty relations, which are again saturated by the GUP coherent states. We argue that this combination of coherent states with Tsallis entropy offers a natural conceptual framework allowing one to study the quasiclassical regime of GUP in terms of nonextensive thermodynamics. We substantiate our claim by discussing the generalization of Verlinde’s entropic force and ensuing implications in the late-inflation epoch. The corresponding dependence of the 𝛽 parameter on cosmological time is derived for the reheating epoch. The obtained 𝛽 is consistent with values predicted by both string-theory models and the naturalness principle. Further salient issues, including the derivation of new 𝛽-dependent expressions for the lowest possible value of the spin and Immirzi parameter in loop quantum gravity and the connection of our proposal with the Magueijo-Smolin doubly special relativity are also discussed. This article provides a more extended and comprehensive treatment of our recent article [Phys. Rev. D 105, L121501 (2022)].
dc.description.sponsorshipWe thank John Klauder, Vladimir Lotoreichik and Pavel Exner for useful discussions and comments on the manuscript. P.J. was in part supported by the FNSPE CTU grant RVO14000. G.G.L. acknowledges the Spanish β€œMinisterio de Universidades” for the awarded Maria Zambrano fellowship and funding received from the European Union - NextGenerationEU. L.P. is grateful to the β€œAngelo Della Riccia” foundation for the awarded fellowship received to support the study at UniversitΒ¨at Ulm. G.G.L. and L.P. acknowledge networking support by the COST Action CA18108
dc.identifier.doihttps://doi.org/10.1103/PhysRevD.108.064024
dc.identifier.issn2470-0029
dc.identifier.urihttps://repositori.udl.cat/handle/10459.1/465928
dc.language.isoeng
dc.publisherAmerican Physical Society
dc.relation.isformatofVersiΓ³ preprint del document publicat a https://doi.org/10.1103/PhysRevD.108.064024
dc.relation.ispartofPhysical Review D particles, fields, gravitation, and cosmology, 2023, vol. 108, nΓΊm. 6, 064024
dc.rights(c) American Physical Society, 2023
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.subjectAtomic, Molecular & Optical
dc.subjectGravitation, Cosmology & Astrophysics
dc.subjectStatistical Physics & Thermodynamics
dc.subjectQuantum Information, Science & Technology
dc.titleCoherent states for generalized uncertainty relations as Tsallis probability amplitudes: New route to nonextensive thermostatistics
dc.typeinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/submittedVersion
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