Abstract
It has been argued that non-Gaussian statistics provide a natural framework to investigate semiclassical effects in the context of Planck-scale deformations of the Heisenberg uncertainty relation. Here we substantiate this point by considering the Unruh effect as a specific playground. By working in the realm of quantum field theory, we reformulate the derivation of the modified Unruh effect from the generalized uncertainty principle (GUP) in the language of the nonextensive Tsallis thermostatistics. We find a nontrivial monotonic relation between the nonextensivity index q and the GUP deformation parameter beta , which generalizes an earlier result obtained in quantum mechanics. We then extend our analysis to black hole thermodynamics. We preliminarily discuss our outcome in the broader context of an effective description of Planck-scale gravitational physics based on Tsallis theory.
Highlights
In the last decades several models of quantum gravity, such as String Theory, Loop Quantum Gravity, Quantum Geometry and Doubly Special Relativity, and heuristic arguments on black hole physics have converged on the idea that the Heisenberg uncertainty principle (HUP) should be amended at Planck scale to account for the emergence of a minimal measurable length [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
It is a well-established fact that a vast class of physical phenomena can be adequately described by distributions deviating from Gaussian statistics
Inspired by the result of [51], in this work we have substantiated the idea that the emergence of a minimal length induced by the generalized uncertainty principle (GUP) introduces a change in the volume of the elementary phase space cell, which can be naturally translated into a departure of the statistics from a pure Gaussian behavior
Summary
In the last decades several models of quantum gravity, such as String Theory, Loop Quantum Gravity, Quantum Geometry and Doubly Special Relativity, and heuristic arguments on black hole physics have converged on the idea that the Heisenberg uncertainty principle (HUP) should be amended at Planck scale to account for the emergence of a minimal measurable length [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. The correspondence between the two frameworks has been investigated concretely in the contexts of Unruh effect [52] and Jeans instability [53], proving that quadratic non-Gaussian statistics produce the same effects as the GUP (1) at the level of the modified Unruh temperature and Jeans mass, respectively. It is important to stress that our approach is conceptually different from that in [51] The latter relies on the comparison between the GUP- and Tsallis-induced corrections at the level of the phase space cell volume and the ensuing effects on the energy/temperature relation.
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