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

Abstract By regarding the Hawking–Bekenstein entropy of Schwarzschild black hole horizons as a non-extensive Tsallis entropy, its formal logarithm, the Renyi 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 Renyi entropy of micro black holes ( q ⩾ 1 + 2 / π 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.

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