Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: new route to non-extensive thermostatistics

• URL: http://arxiv.org/abs/2308.12368v1
• Date: Wed, 23 Aug 2023 18:16:15 GMT
• Title: Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: new route to non-extensive thermostatistics
• Authors: Petr Jizba, Gaetano Lambiase, Giuseppe Gaetano Luciano and Luciano Petruzziello
• Abstract summary: We study coherent states associated to a generalized uncertainty principle (GUP) We argue that this combination of coherent states with Tsallis entropy offers a natural conceptual framework allowing to study GUP in terms of non-extensive thermodynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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)].

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