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The R\'enyi and Tsallis entropies are discussed as possible alternatives tothe Bekenstein-Hawking area-law entropy. It is pointed out how replacing theentropy notion, but not the Hawking temperature and the thermodynamical energymay render the whole black hole thermodynamics inconsistent. The possibility torelate the R\'enyi and Tsallis entropies with the quantum gravity correctedBekenstein-Hawking entropy is discussed.

Area-law versus R\'enyi and Tsallis black hole entropies