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Scale Invariance and Symmetry Relationships In Non-Extensive Statistical Mechanics

Mark Fleischer
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Abstract

This 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.

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Mark Fleischer. 2005-01-12. Scale Invariance and Symmetry Relationships In Non-Extensive Statistical Mechanics. https://arxiv.org/abs/cond-mat/0501293

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