We have presented a new axiomatic derivation of Shannon entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function. We have then modified Shannon entropy to take account of observational uncertainty.The modified entropy reduces, in the limiting case, to the form of Shannon differential entropy. As an application, we have de...

An approach to the Shannon and Rényi entropy maximization problems with constraints on the mean and law invariant deviation measure for a random variable has been developed. The approach is based on the representation of law invariant deviation measures through corresponding convex compact sets of nonnegative concave functions. A solution to the problem has been shown to have an alpha-concave d...

Within the present advanced review on the meaning, interpretation and applications of the so-called ’complexity’, different order-uncertainty planes emboding relevant information-theoretic magnitudes are studied in order to analyse the information content of the position and momentum electron densities of several atomic systems, including neutral atoms, singly-charged ions and isoelectronic ser...

Current definition of high-entropy alloys (HEAs) is commonly based on the configurational entropy. But this depends only chemical composition a HEA and therefore cannot distinguish information content that encoded in various local atomic arrangements measurable by Shannon entropy theory. Here, inspired finding two-dimensional (2D) Sudoku matrices exhibit higher average than 2D random matrix cou...