R\'enyi entropy for particle systems as an instrument to enlarge the Boltzmannian concept of entropy: some holographic perspectives

TL;DR

This paper explores the Rényi entropy's physical interpretation in particle systems, providing explicit formulas and constraints that extend the classical Boltzmannian entropy concept within holographic frameworks.

Contribution

It offers a general explicit representation of Rényi entropy for various particle fluids and establishes physical bounds on its order parameter based on thermodynamics and holography.

Findings

Derived explicit Rényi entropy formulas for particle systems.

Established thermodynamic and holographic bounds on Rényi entropy.

Extended the Boltzmannian entropy concept using holographic perspectives.

Abstract

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.