Nonextensive statistical mechanics and high energy physics

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, black holes and others. In addition to that, we clarify and illustrate the neat distinction that exists between Levy distributions and q-exponential ones, a point which occasionally causes some confusion in the literature, very particularly in the LHC literature.