 The Gimath-XMLNS-Equals-Display-Equals-Inline-PASQ non-additive entropy has been extensively studied over the past few decades. It was originally proposed as a generalization of the Boltzmann-Gibbs entropy, and has since been used to model systems with multiple degrees of freedom. One of its key features is the connection between the Gimath-XMLNS-Equals-Display-Equals-Inline-PASQ canonical distribution and the micro-canonical ensemble. This connection was first discovered in 1994, and has since been further explored by many researchers. In this paper, we review some of these works, focusing on those which investigate the Gimath-XMLNS-Equals-Display-Equals-Inline-PASQ micro-canonical connection. This article was authored by Angel R. Plastino and Angel O. Plastino.