Tsallis statistics and generalized uncertainty principle
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 w...
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2021-07-01
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Series: | European Physical Journal C: Particles and Fields |
Online Access: | https://doi.org/10.1140/epjc/s10052-021-09486-x |
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doaj-38de619703cc4f4c8660242662b297fe2021-08-01T11:12:37ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522021-07-0181711210.1140/epjc/s10052-021-09486-xTsallis statistics and generalized uncertainty principleGiuseppe Gaetano Luciano0Dipartimento di Fisica, Università di SalernoAbstract 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 $$\beta $$ β , 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.https://doi.org/10.1140/epjc/s10052-021-09486-x |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Giuseppe Gaetano Luciano |
spellingShingle |
Giuseppe Gaetano Luciano Tsallis statistics and generalized uncertainty principle European Physical Journal C: Particles and Fields |
author_facet |
Giuseppe Gaetano Luciano |
author_sort |
Giuseppe Gaetano Luciano |
title |
Tsallis statistics and generalized uncertainty principle |
title_short |
Tsallis statistics and generalized uncertainty principle |
title_full |
Tsallis statistics and generalized uncertainty principle |
title_fullStr |
Tsallis statistics and generalized uncertainty principle |
title_full_unstemmed |
Tsallis statistics and generalized uncertainty principle |
title_sort |
tsallis statistics and generalized uncertainty principle |
publisher |
SpringerOpen |
series |
European Physical Journal C: Particles and Fields |
issn |
1434-6044 1434-6052 |
publishDate |
2021-07-01 |
description |
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 $$\beta $$ β , 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. |
url |
https://doi.org/10.1140/epjc/s10052-021-09486-x |
work_keys_str_mv |
AT giuseppegaetanoluciano tsallisstatisticsandgeneralizeduncertaintyprinciple |
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