Symmetric deformed binomial distributions: An analytical example where the Boltzmann-Gibbs entropy is not extensive

DOI10.1063/1.4939917zbMath1357.62078OpenAlexW2325122971MaRDI QIDQ2795576

H. Bergeron, Evaldo M. F. Curado, Jean-Pierre Gazeau, Ligia M. C. S. Rodrigues

Publication date: 21 March 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/1cb0eb5fc78c11a6f5f496e7f19ee047af0d725b

zbMATH Keywords

asymptotic behaviorBoltzmann-Gibbs entropyRényi entropybinomial distributions

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Approximations to statistical distributions (nonasymptotic) (62E17) Measures of information, entropy (94A17) Statistical thermodynamics (82B30) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Cites Work

• A Mathematical Theory of Communication
• On a generalization of the binomial distribution and its Poisson-like limit
• Extensivity of Rényi entropy for the Laplace-de Finetti distribution
• On the Lambert \(w\) function
• GENERALIZED BINOMIAL DISTRIBUTIONS
• Connection between Dirichlet distributions and a scale-invariant probabilistic model based on Leibniz-like pyramids
• Emergence of q-statistical functions in a generalized binomial distribution with strong correlations
• Symmetric generalized binomial distributions
• Generating functions for generalized binomial distributions
• Large deviations
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