R\'enyi Entropy of Zeta-Urns

TL;DR

This paper analytically computes the Re9nyi entropy for the zeta-urn model, linking its singularities to thermodynamic properties and exploring how they vary with model parameters and entropy order.

Contribution

It provides an analytical framework for calculating Re9nyi entropy in the zeta-urn model and characterizes its singularities based on thermodynamic potential.

Findings

Identifies singularities in Re9nyi entropy related to thermodynamic potential

Classifies behaviors of Re9nyi entropy depending on model parameters

Establishes connection between entropy singularities and free energy density

Abstract

We calculate analytically the Renyi entropy for the zeta-urn model with a Gibbs measure definition of the micro-state probabilities. This allows us to obtain the singularities in the R\'enyi entropy from those of the thermodynamic potential, which is directly related to the free energy density of the model. We enumerate the various possible behaviours of the R\'enyi entropy and its singularities, which depend on both the value of the power law in the zeta-urn and the order of the R\'enyi entropy under consideration