Entropic descriptor of a complex behaviour

Abstract

We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum possible value Smax and its minimum possible value Smin. When these two departures are similar to each other, the statistical complexity is maximal. We apply the new concept to the variability, over a range of length scales, of spatial or grey-level pattern arrangements in simple models. The pertinent results confirm the fact that a highly non-trivial, length-scale dependence of the entropic descriptor makes it an adequate complexity-measure, able to distinguish between structurally distinct configurational macrostates with the same degree of disorder.

14 pages, 7 figures, extended version

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• A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions
• Decomposable multiphase entropic descriptor
• Statistical Reconstruction of Microstructures Using Entropic Descriptors
• Low-cost approximate reconstructing of heterogeneous microstructures
• A proposal about the meaning of scale, scope and resolution in the context of the interpretation process