04034nam 2200889z- 450 991056646170332120220506(CKB)5680000000037764(oapen)https://directory.doabooks.org/handle/20.500.12854/80958(oapen)doab80958(EXLCZ)99568000000003776420202205d2022 |y 0engurmn|---annantxtrdacontentcrdamediacrrdacarrierThe Statistical Foundations of EntropyBaselMDPI - Multidisciplinary Digital Publishing Institute20221 online resource (182 p.)3-0365-3557-8 3-0365-3558-6 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.Mathematics & sciencebicsscResearch & information: generalbicsscadaptive Type-II progressive hybrid censoring schemeBayesian estimationBayesian inferencecalibration invarianceconfidence intervalcritical phenomenadistributional weighted regressionecological inferenceentropic uncertainty relationsentropyescort probabilitiesgaussian entropygeneralized Bilal distributiongeneralized cross entropygeneralized entropiesGENERICKolmogorov-Nagumo averagesLagrange multiplierslandsberg-vedral entropyLindley's approximationMarkov chain Monte Carlo methodmatrix adjustmentMaxEnt distributionmaximum entropymaximum entropy principlemaximum likelihood estimationmultiscale thermodynamicsn/anon-Diophantine arithmeticnon-equilibrium thermodynamicsnon-Newtonian calculusquantum metrologyrenormalizationrényi entropyRényi entropysharma-mittal entropytsallis entropyTsallis entropyupdating probabilitiesvariational entropyα-channel capacityα-mutual informationMathematics & scienceResearch & information: generalJizba Petredt618869Korbel JanedtJizba PetrothKorbel JanothBOOK9910566461703321The Statistical Foundations of Entropy3040910UNINA