The extended uncertainty principle inspires the R\'{e}nyi entropy

Understand

We use the extended uncertainty principle (EUP) in order to obtain the R\'{e}nyi entropy for a black hole (BH).

• The result implies that the non-extensivity parameter, appeared in the R\'{e}nyi entropy formalism, may be evaluated from the considerations which lead to EUP.
• It is also shown that, for excited BHs, the R\'{e}nyi entropy is a function of the BH principal quantum number, i.e.
• the BH quantum excited state.