  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 $\mathcal{B}$-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.
