The Statistical Foundations of Entropy

• Other Authors: Jizba, Petr (Editor), Korbel, Jan (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2022
• Subjects: Research & information: general; Mathematics & science; ecological inference; generalized cross entropy; distributional weighted regression; matrix adjustment; entropy; critical phenomena; renormalization; multiscale thermodynamics; GENERIC; non-Newtonian calculus; non-Diophantine arithmetic; Kolmogorov-Nagumo averages; escort probabilities; generalized entropies; maximum entropy principle; MaxEnt distribution; calibration invariance; Lagrange multipliers; generalized Bilal distribution; adaptive Type-II progressive hybrid censoring scheme; maximum likelihood estimation; Bayesian estimation; Lindley's approximation; confidence interval; Markov chain Monte Carlo method; Rényi entropy; Tsallis entropy; entropic uncertainty relations; quantum metrology; non-equilibrium thermodynamics; variational entropy; rényi entropy; tsallis entropy; landsberg-vedral entropy; gaussian entropy; sharma-mittal entropy; α-mutual information; α-channel capacity; maximum entropy; Bayesian inference; updating probabilities; n/a
• Online Access: DOAB: download the publication; DOAB: description of the publication

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...