Statistical mechanics characterization of spatio-compositional inhomogeneity

On the basis of a model system of pillars built of unit cubes, a two-component entropic measure for the multiscale analysis of spatio-compositional inhomogeneity is proposed. It quantifies the statistical dissimilarity per cell of the actual configurational macrostate and the theoretical reference one that maximizes entropy. Two kinds of disorder compete: (i) the spatial one connected with possible positions of pillars inside a cell (the first component of the measure), (ii) the compositional one linked to compositions of each local sum of their integer heights into a number of pillars occupying the cell (the second component). As both the number of pillars and sum of their heights are conserved, an upper limit for a pillar height hmax occurs. If due to a further constraint there is the more demanding limit h⩽h∗