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It is pointed out that the generalized thermodynamics introduced by Tsallis [J. Stat. Phys. 52 (1988) 479] provides a natural frame for the extension of the thermodynamical formalism of symbolic dynamics. The statistical structure of 1D fractal long-range correlation sequences is investigated using an n-tuple Zipf analysis. The generalized form of the Zipf-Mandelbrot law can be obtained using the maximum entropy principle within the frame of Tsallis thermodynamics, with the Zipf exponent ξ = 1 (q − 1) where q is the entropic index, if the frequency of a word is associated with the probability and the rank with the energy.