Substitution systems and nonextensive statistics

V. García-Morales

Physica A: Statistical Mechanics and its Applications, 2015, vol. 440, issue C, 110-117

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 Nk symbols also within the alphabet (with Nk, a natural number, being the length of the kth block of the substitution). The dynamics of these systems leads naturally to fractals and self-similarity. By using B-calculus (García-Morales, 2012) 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.

Keywords: Symbolic dynamics; Fractals; Tilings; Tsallis entropy; Complexity; Irreversibility (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:440:y:2015:i:c:p:110-117

DOI: 10.1016/j.physa.2015.07.035

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