Local Entropy Characterization of Correlated Random Microstructures

TL;DR

This paper establishes a rigorous link between two local entropy measures used to describe correlated microstructures in porous media and heterogeneous systems, demonstrating their equivalence at high resolution and illustrating their usefulness through examples.

Contribution

It provides a formal connection between two previously separate local entropy descriptors for microstructures, enhancing understanding of their relationship and applicability.

Findings

Entropy lengths converge at high resolution.

The local entropy concept is demonstrated as useful.

Examples show the descriptors' effectiveness.

Abstract

A rigorous connection is established between the local porosity entropy introduced by Boger et al. (Physica A 187, 55 (1992)) and the configurational entropy of Andraud et al. (Physica A 207, 208 (1994)). These entropies were introduced as morphological descriptors derived from local volume fluctuations in arbitrary correlated microstructures occuring in porous media, composites or other heterogeneous systems. It is found that the entropy lengths at which the entropies assume an extremum become identical for high enough resolution of the underlying configurations. Several examples of porous and heterogeneous media are given which demonstrate the usefulness and importance of this morphological local entropy concept.