Self-organization can be envisioned as a process of formation of recognizable patterns upon the injection of energy into and the efficient expulsion of energy from a given physical system. A Z-pinch is an electric discharge between two terminals within a given gas environment, providing the context for the possible formation of geometrical structures of the ionized gas with free electrons: a plasma. These plasma structures may last longer in time due to the efficient expulsion of entropy, and the higher gain in energy. Sustained existence of a z-pinch plasma may serve for the purposes of generation of high-rate, high-density neutron fluxes, which in turn may be used for neutron imaging, material studies and material treatment, like sputtering, among other possible uses. In this work it has been shown evidence for the correlation between the highest input of energy and the highest output of entropy, with the spontaneous formation of plasma structures.