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The use of the celebrated Boltzmann-Gibbs entropy and statistical mechanics is justified for ergodic-like systems. In contrast, complex systems typically require more powerful theories. We will provide a brief introduction to nonadditive entropies (characterized by indices like q, which, in the q → 1 limit, recovers the standard Boltzmann-Gibbs entropy) and associated nonextensive statistical mechanics. We then present some recent applications to systems such as high-energy collisions, blackdoi:10.1051/epjconf/20147100132 fatcat:gar22tce7rfgpdrtvbz2ynglmu