Non-Additive Entropy Formulas: Motivation and Derivations.

Entropy is a great tool in thermodynamics and statistical physics [...].

Non-Additive Entropy Composition Rules Connected with Finite Heat-Bath Effects.

Mathematical generalizations of the additive Boltzmann-Gibbs-Shannon entropy formula have been numerous since the 1960s. In this paper we seek an interpretation of the Rényi and Tsallis q-entropy formulas single parameter in terms of physical properties of a finite capacity heat-bath and fluctuations of temperature. Ideal gases of non-interacting particles are used as a demonstrating example.

f-Gintropy: An Entropic Distance Ranking Based on the Gini Index.

We consider an entropic distance analog quantity based on the density of the Gini index in the Lorenz map, i.e., gintropy. Such a quantity might be used for pairwise mapping and ranking between various countries and regions based on income and wealth inequality. Its generalization to f-gintropy, using a function of the income or wealth value, distinguishes between regional inequalities more sensitively than the original construction.