2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/25664This article extends results described in a recent article detailing a structural scale invariance property of the simulated annealing (SA) algorithm. These extensions are based on generalizations of the SA algorithm based on Tsallis statistics and a non-extensive form of entropy. These scale invariance properties show how arbitrary aggregations of energy levels retain certain mathematical characteristics. In applying the non-extensive forms of statistical mechanics to illuminate these scale invariance properties, an interesting energy transformation is revealed that has a number of potentially useful applications. This energy transformation function also reveals a number of symmetry properties. Further extensions of this research indicate how this energy transformation function relates to power law distributions and potential application for overcoming the so-called ``broken ergodicity'' problem prevalent in many computer simulations of critical phenomena.23 pages, 3 figuresStatistical Mechanicstext