Rényi Entropy of Zeta Urns

Piotr Bialas; Zdzislaw Burda; Desmond A. Johnston

doi:10.1103/PhysRevE.108.064108

Rényi Entropy of Zeta Urns

Piotr Bialas, Zdzislaw Burda, Desmond A. Johnston

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Abstract

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

Original language	English
Article number	064108
Journal	Physical Review E
Volume	108
Issue number	6
DOIs	https://doi.org/10.1103/PhysRevE.108.064108
Publication status	Published - 5 Dec 2023

Keywords

cond-mat.stat-mech
math-ph
math.MP

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abstract = "We calculate analytically the R{\'e}nyi entropy for the zeta-urn model with a Gibbs measure definition of the microstate probabilities. This allows us to obtain the singularities in the R{\'e}nyi entropy from those of the thermodynamic potential, which is directly related to the free-energy density of the model. We enumerate the various possible behaviors of the R{\'e}nyi entropy and its singularities, which depend on both the value of the power law in the zeta urn and the order of the R{\'e}nyi entropy under consideration.",

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N2 - We calculate analytically the Rényi entropy for the zeta-urn model with a Gibbs measure definition of the microstate probabilities. This allows us to obtain the singularities in the Rényi entropy from those of the thermodynamic potential, which is directly related to the free-energy density of the model. We enumerate the various possible behaviors of the Rényi entropy and its singularities, which depend on both the value of the power law in the zeta urn and the order of the Rényi entropy under consideration.

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

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Rényi Entropy of Zeta Urns

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