  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.
