 The non-additive entropy SQ has been used to study a variety of systems that do not satisfy the assumptions of the Boltzmann, Gibbs, BG, statistical mechanics. This includes systems that are not ergodic or have other properties that make them unsuitable for the BG approach. The entropy SQ can be applied to both Hamiltonian and non-Hamiltonian systems, and it has been used to analyze probability distributions low-dimensional non-linear dynamical systems and long-range interacting many-body classical Hamiltonian systems. Recent studies have demonstrated its usefulness in analyzing natural, artificial, and social systems. This article was authored by Konstantino Tsalis.