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The goal of this paper is to develop an estimate for the entropy of randomlong-range correlated symbolic sequences with elements belonging to a finitealphabet. As a plausible model, we use the high-order additive stationaryergodic Markov chain. Supposing that the correlations between random elementsof the chain are weak we express the differential entropy of the sequence bymeans of the symbolic pair correlation function. We also examine an algorithmfor estimating the differential entropy of finite symbolic sequences. We showthat the entropy contains two contributions, the correlation and fluctuationones. The obtained analytical results are used for numerical evaluation of theentropy of written English texts and DNA nucleotide sequences. The developedtheory opens the way for constructing a more consistent and sophisticatedapproach to describe the systems with strong short- and weak long-rangecorrelations.

Entropy and long-range correlations in random symbolic sequences