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Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: new route to non-extensive thermostatistics
- Source :
- Phys. Rev. D 108, 064024 (2023)
- Publication Year :
- 2023
-
Abstract
- We study coherent states associated to a generalized uncertainty principle (GUP). We separately analyze the cases of positive and negative deformation parameter $\beta$, showing that the ensuing probability distribution is a Tsallis distribution whose non-extensivity parameter $q$ is monotonically related to $\beta$. Moreover, for $\beta <0$ (corresponding to $q<1$), 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 to study quasi-classical regime of GUP in terms of non-extensive thermodynamics. We substantiate our claim by discussing generalization of Verlinde's entropic force and ensuing implications in the late-inflation epoch. Corresponding dependence of the $\beta$ parameter on cosmological time is derived for the reheating epoch. The obtained $\beta$ is consistent with values predicted by both string-theory models and the naturalness principle. Further salient issues, including derivation of new $\beta$-dependent expressions for the lowest possible value of the spin and Immirzi parameter in Loop Quantum Gravity, and 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 letter [Phys. Rev. D 105, L121501 (2022)].<br />Comment: 25 pages, 4 figures, accepted to Physical Review D
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. D 108, 064024 (2023)
- Publication Type :
- Report
- Accession number :
- edsarx.2308.12368
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevD.108.064024