Nonadditive entropy and nonextensive statistical mechanics -an overview after 20 years

Statistical mechanics constitutes one of the pillars of contemporary physics. Recognized as such - together with mechanics (classical, quantum, relativistic), electromagnetism and thermodynamics -, it is one of the mandatory theories studied at virtually all the intermediate-and advanced-level courses of physics around the world. As it normally happens with such basic scientific paradigms, it is placed at a crossroads of various other branches of knowledge. In the case of statistical mechanics, the standard theory - hereafter referred to as the Boltzmann-Gibbs (BG) statistical mechanics - exhi...