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The R\'enyi entropy is a mathematical generalization of the concept of entropy and it encodes the total information of a system as a funtion of its order parameter $\alpha$. The meaning of the R\'enyi entropy in physics is not completely enstablished: here we determined a general and explicit representation of the R\'enyi entropy for whichever fluid of particles and spin-statistics, in the mechanical statistics framework. This allowed us to put physical constraints to the R\'enyi order $\alpha$, from main thermodynamical relations and entropy bounds of the holographic theories, defining how much we can enlarge the Boltmannian concept of entropy.

Rényi entropy for particle systems as an instrument to enlarge the Boltzmannian concept of entropy: Some holographic perspectives