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The Statistical Foundations of Entropy
Petr Jizba (editor) and Jan Korbel (editor)
2022
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In the last two decades, the understanding of complex dynamical systems underwent important conceptual shifts. The catalyst was the infusion of new ideas from the theory of critical phenomena (scaling laws, renormalization group, etc.), (multi)fractals and trees, random matrix theory, network theory, and non-Shannonian information theory. The usual Boltzmann–Gibbs statistics were proven to be grossly inadequate in this context. While successful in describing stationary systems characterized by ergodicity or metric transitivity, Boltzmann–Gibbs statistics fail to reproduce the complex statistical behavior of many real-world systems in biology, astrophysics, geology, and the economic and social sciences.The aim of this Special Issue was to extend the state of the art by original contributions that could contribute to an ongoing discussion on the statistical foundations of entropy, with a particular emphasis on non-conventional entropies that go significantly beyond Boltzmann, Gibbs, and Shannon paradigms. The accepted contributions addressed various aspects including information theoretic, thermodynamic and quantum aspects of complex systems and found several important applications of generalized entropies in various systems.
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Keywords
- adaptive Type-II progressive hybrid censoring scheme
- Bayesian estimation
- Bayesian inference
- calibration invariance
- confidence interval
- critical phenomena
- distributional weighted regression
- ecological inference
- entropic uncertainty relations
- Entropy
- escort probabilities
- gaussian entropy
- generalized Bilal distribution
- generalized cross entropy
- generalized entropies
- GENERIC
- Kolmogorov–Nagumo averages
- Lagrange multipliers
- landsberg—vedral entropy
- Lindley’s approximation
- Markov chain Monte Carlo method
- Mathematics & science
- matrix adjustment
- MaxEnt distribution
- Maximum entropy
- maximum entropy principle
- maximum likelihood estimation
- multiscale thermodynamics
- n/a
- non-Diophantine arithmetic
- non-equilibrium thermodynamics
- non-Newtonian calculus
- quantum metrology
- Reference, information & interdisciplinary subjects
- renormalization
- Rényi entropy
- Research & information: general
- sharma—mittal entropy
- Tsallis entropy
- updating probabilities
- variational entropy
- α-channel capacity
- α-mutual information
Links
DOI: 10.3390/books978-3-0365-3558-6Editions