Information entropy of complex structures

Abstract

The information entropy function provides a sensitive measure of the complexity of a multi-component material system, where “complexity” refers to the range of length scales over which morphological features are present. This is demonstrated for an evolving, two-phase microstructure simulated by a population of interacting particles on a two-dimensional surface. The information entropy increases at all length scales as the initially random configuration of particles evolves to produce a distribution of ramified clusters. Maxima in the normalized information entropy function, which is obtained by subtracting the information entropy of a perfectly random configuration from that of the clustered configuration, occur at length scales for which the system most differs from a random configuration, while minima occur at length scales for which the system is periodic or relatively ordered. Besides analysis of complex microstructures, information entropy is useful in detecting features present in any collection of data.