TY - BOOK ID - 135061671 TI - The Statistical Foundations of Entropy AU - Jizba, Petr AU - Korbel, Jan PY - 2022 PB - Basel MDPI - Multidisciplinary Digital Publishing Institute DB - UniCat KW - ecological inference KW - generalized cross entropy KW - distributional weighted regression KW - matrix adjustment KW - entropy KW - critical phenomena KW - renormalization KW - multiscale thermodynamics KW - GENERIC KW - non-Newtonian calculus KW - non-Diophantine arithmetic KW - Kolmogorov–Nagumo averages KW - escort probabilities KW - generalized entropies KW - maximum entropy principle KW - MaxEnt distribution KW - calibration invariance KW - Lagrange multipliers KW - generalized Bilal distribution KW - adaptive Type-II progressive hybrid censoring scheme KW - maximum likelihood estimation KW - Bayesian estimation KW - Lindley’s approximation KW - confidence interval KW - Markov chain Monte Carlo method KW - Rényi entropy KW - Tsallis entropy KW - entropic uncertainty relations KW - quantum metrology KW - non-equilibrium thermodynamics KW - variational entropy KW - rényi entropy KW - tsallis entropy KW - landsberg—vedral entropy KW - gaussian entropy KW - sharma—mittal entropy KW - α-mutual information KW - α-channel capacity KW - maximum entropy KW - Bayesian inference KW - updating probabilities KW - n/a KW - Kolmogorov-Nagumo averages KW - Lindley's approximation KW - Rényi entropy KW - rényi entropy KW - landsberg-vedral entropy KW - sharma-mittal entropy UR - https://www.unicat.be/uniCat?func=search&query=sysid:135061671 AB - 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. ER -