Symbolic dynamics of fully developed chaos

By discerning levels k of statistical description it is shown that the level-k Boltzmann entropy h(k) ∝ log (# possibilities on level k) of two-symbol sequences equals the information theoretical conditional entropy kS(k)-(k-1)S(k-1), with S(k) the average Shannon entropy on level k. A mixing measure μ is introduced by means of an appropriate demixing procedure. From the properties of the two-symbol sequence an expression for a symbolic 2 x 2 correlation matrix is derived.