  We study the N-step binary stationary ergodic Markov chain and analyze its
differential entropy. Supposing that the correlations are weak we express the
conditional probability function of the chain through the pair correlation
function and represent the entropy as a functional of the pair correlator.
Since the model uses the two-point correlators instead of the block
probability, it makes it possible to calculate the entropy of strings at much
longer distances than using standard methods. A fluctuation contribution to the
entropy due to finiteness of random chains is examined. This contribution can
be of the same order as its regular part even at the relatively short lengths
of subsequences. A self-similar structure of entropy with respect to the
decimation transformations is revealed for some specific forms of the pair
correlation function. Application of the theory to the DNA sequence of the R3
chromosome of Drosophila melanogaster is presented.
