04001nam 2200865z- 450 991056646170332120231214133252.0(CKB)5680000000037764(oapen)https://directory.doabooks.org/handle/20.500.12854/80958(EXLCZ)99568000000003776420202205d2022 |y 0engurmn|---annantxtrdacontentcrdamediacrrdacarrierThe Statistical Foundations of EntropyBaselMDPI - Multidisciplinary Digital Publishing Institute20221 electronic 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.Research & information: generalbicsscMathematics & sciencebicsscecological inferencegeneralized cross entropydistributional weighted regressionmatrix adjustmententropycritical phenomenarenormalizationmultiscale thermodynamicsGENERICnon-Newtonian calculusnon-Diophantine arithmeticKolmogorov-Nagumo averagesescort probabilitiesgeneralized entropiesmaximum entropy principleMaxEnt distributioncalibration invarianceLagrange multipliersgeneralized Bilal distributionadaptive Type-II progressive hybrid censoring schememaximum likelihood estimationBayesian estimationLindley's approximationconfidence intervalMarkov chain Monte Carlo methodRényi entropyTsallis entropyentropic uncertainty relationsquantum metrologynon-equilibrium thermodynamicsvariational entropyrényi entropytsallis entropylandsberg-vedral entropygaussian entropysharma-mittal entropyα-mutual informationα-channel capacitymaximum entropyBayesian inferenceupdating probabilitiesResearch & information: generalMathematics & scienceJizba Petredt618869Korbel JanedtJizba PetrothKorbel JanothBOOK9910566461703321The Statistical Foundations of Entropy3040910UNINA