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RESEARCH PRODUCT
Substitution systems and nonextensive statistics
Vladimir García-moralesVladimir García-moralessubject
Statistics and ProbabilityDiscrete mathematicsTsallis entropymedia_common.quotation_subjectSymbolic dynamicsBlock (permutation group theory)Substitution (algebra)Natural numberSecond law of thermodynamicsCondensed Matter PhysicsLimit (mathematics)Constant (mathematics)Mathematicsmedia_commondescription
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 N k symbols also within the alphabet (with N k , a natural number, being the length of the k th block of the substitution). The dynamics of these systems leads naturally to fractals and self-similarity. By using B -calculus (Garcia-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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-12-01 | Physica A: Statistical Mechanics and its Applications |