Abstract: Complexity of natural, artificial and social systems can be studied from many perspectives. It is not the lesser the one which uses concepts of statistical mechanics, very especially of its modern version — nonextensive statistical mechanics — based on nonadditive entropies, which generalize the celebrated Boltzmann-Gibbs-Shannon-von Neumann entropy. I will briefly review the physical motivations of this generalization and present some illustrative applications in various areas of knowledge. From the time, around 2005, when Murray Gell-Mann and I were investigating the so-called q-triplets, some better understanding has been achieved, which I will describe as well.
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