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

The Rényi entropy is a mathematical generalization of the concept of entropy and it encodes the total information of a system as a function of its order parameter α. The meaning of the Rényi entropy in physics is not completely established. Here we determined a general and explicit representation of the Rényi entropy for whichever fluid of particles and spin-statistics in the mechanical statistics framework. This allowed us to put physical constraints to the Rényi order α, from main thermodynamic relations and entropy bounds of the holographic theories, defining how much we can enlarge the Boltzmannian concept of entropy.