A q-parameter bound for particle spectra based on black hole thermodynamics with R\'enyi-entropy
Abstract
By regarding the Hawking-Bekenstein entropy of Schwarzschild black hole horizons as a non-extensive Tsallis entropy, its formal logarithm, the R\'enyi 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 R\'enyi entropy of micro black holes, (q >= 1 + 2/pi^2), 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.
Keywords
Cite
@article{arxiv.1309.4261,
title = {A q-parameter bound for particle spectra based on black hole thermodynamics with R\'enyi-entropy},
author = {Tamás S. Biró and Viktor G. Czinner},
journal= {arXiv preprint arXiv:1309.4261},
year = {2013}
}
Comments
5 pages, 1 figure, to be published in Phys. Lett. B. arXiv admin note: text overlap with arXiv:1011.3442