Dynamic entropies, long-range correlations, and fluctuations in complex linear structures

TL;DR

This paper analyzes complex linear structures like books and DNA sequences using entropy measures, correlation functions, and spectral analysis to detect long-range correlations and fluctuations across different scales.

Contribution

It compares various measures of long-range correlations in symbolic sequences and demonstrates their scale-dependent sensitivities through shuffling experiments.

Findings

Higher order Shannon entropies follow a root law.

All measures can detect long-range correlations.

Correlations extend over hundreds to thousands of letters.

Abstract

We investigate symbolic sequences and in particular information carriers as e.g. books and DNA-strings. First the higher order Shannon entropies are calculated, a characteristic root law is detected. Then the algorithmic entropy is estimated by using Lempel-Ziv compression algorithms. In the third section the correlation function for distant letters, the low frequency Fourier spectrum and the characteristic scaling exponents are calculated. We show that all these measures are able to detect long-range correlations. However, as demonstrated by shuffling experiments, different measures operate on different length scales. The longest correlations found in our analysis comprise a few hundreds or thousands of letters and may be understood as long-wave fluctuations of the composition.