A q-parameter bound for particle spectra based on black hole thermodynamics with Rényi entropy

By regarding the Hawking–Bekenstein entropy of Schwarzschild black hole horizons as a non-extensive Tsallis entropy, its formal logarithm, the Rényi entropy, is considered. The resulting temperature – horizon radius relation has the same form as the one obtained from a (3+1)-dimensional black hole i...

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Bibliographic Details
Published in:Physics letters. B 2013-11, Vol.726 (4-5), p.861-865
Main Authors: Biró, Tamás S., Czinner, Viktor G.
Format: Article
Language:English
Subjects:
Accelerators
Black hole thermodynamics
Black holes (astronomy)
Coalescing
Elementary particles
Entropy
Hadrons
Heavy ion collisions
Horizon
Non-extensive entropy
Spectra
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Summary:By regarding the Hawking–Bekenstein entropy of Schwarzschild black hole horizons as a non-extensive Tsallis entropy, its formal logarithm, the Rényi entropy, is considered. The resulting temperature – horizon radius relation has the same form as the one obtained from a (3+1)-dimensional black hole in anti-de Sitter space using the original entropy formula. In both cases the temperature has a minimum. A semi-classical estimate of the horizon radius at this minimum leads to a Bekenstein bound for the q-parameter in the Rényi entropy of micro black holes (q⩾1+2/π2), which is surprisingly close to fitted q-parameters of cosmic ray spectra and power-law distribution of quarks coalescing to hadrons in high energy accelerator experiments.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2013.09.032