Substitution Systems and Nonextensive Statistics
Abstract
Substitution systems evolve in time by generating sequences of symbols from a finite alphabet: At a certain iteration step, the existing symbols are systematically replaced by blocks of symbols also within the alphabet (with , a natural number, being the length of the -th block of the substitution). The dynamics of these systems leads naturally to fractals and self-similarity. By using -calculus [V. Garcia-Morales, Phys. Lett. A 376 (2012) 2645] universal maps for deterministic substitution systems both of constant and non-constant length, are formulated in 1D. It is then shown how these systems can be put in direct correspondence with Tsallis entropy. A `Second Law of Thermodynamics' is also proved for these systems in the asymptotic limit of large words.
Cite
@article{arxiv.1309.5254,
title = {Substitution Systems and Nonextensive Statistics},
author = {Vladimir Garcia-Morales},
journal= {arXiv preprint arXiv:1309.5254},
year = {2015}
}
Comments
17 pages, 2 figures, major improvements introduced in revised version. Almost 10 pages of the prolix and verbose previous version have been spared and a new section has been added instead. In the latter, the problem of substitution systems of non constant length is now tackled as well. Accepted to Physica A