Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: New route to nonextensive thermostatistics
dc.contributor.author | Jizba, P. | |
dc.contributor.author | Lambiase, G. | |
dc.contributor.author | Luciano, Giuseppe Gaetano | |
dc.contributor.author | Petruzziello, L. | |
dc.date.accessioned | 2024-06-12T08:50:36Z | |
dc.date.available | 2024-06-12T08:50:36Z | |
dc.date.issued | 2023 | |
dc.description.abstract | We study coherent states associated with a generalized uncertainty principle (GUP). We separately analyze the cases of positive and negative deformation parameter π½, showing that the ensuing probability distribution is a Tsallis distribution whose nonextensivity parameter π is monotonically related to π½. Moreover, for π½<0 (corresponding to π<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 Verlindeβs entropic force and ensuing implications in the late-inflation epoch. The corresponding dependence of the π½ parameter on cosmological time is derived for the reheating epoch. The obtained π½ is consistent with values predicted by both string-theory models and the naturalness principle. Further salient issues, including the derivation of new π½-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.sponsorship | We 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 βMinisterio de Universidadesβ for the awarded Maria Zambrano fellowship and funding received from the European Union - NextGenerationEU. L.P. is grateful to the βAngelo Della Ricciaβ 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.doi | https://doi.org/10.1103/PhysRevD.108.064024 | |
dc.identifier.issn | 2470-0029 | |
dc.identifier.uri | https://repositori.udl.cat/handle/10459.1/465928 | |
dc.language.iso | eng | |
dc.publisher | American Physical Society | |
dc.relation.isformatof | VersiΓ³ preprint del document publicat a https://doi.org/10.1103/PhysRevD.108.064024 | |
dc.relation.ispartof | Physical Review D particles, fields, gravitation, and cosmology, 2023, vol. 108, nΓΊm. 6, 064024 | |
dc.rights | (c) American Physical Society, 2023 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
dc.subject | Atomic, Molecular & Optical | |
dc.subject | Gravitation, Cosmology & Astrophysics | |
dc.subject | Statistical Physics & Thermodynamics | |
dc.subject | Quantum Information, Science & Technology | |
dc.title | Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: New route to nonextensive thermostatistics | |
dc.type | info:eu-repo/semantics/article | |
dc.type.version | info:eu-repo/semantics/submittedVersion |