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 SmaxS 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, a feature that makes it a good tool for discerning structures in complex patterns.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, a feature that makes it a good tool for discerning structures in complex patterns.