1 research outputs found
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, the upper limit for a pillar
height hmax occurs. If due to a further constraint there is the more demanding
limit h <= h* < hmax, the exact number of restricted compositions can be then
obtained only through the generating function. However, at least for systems
with exclusively composition degrees of freedom, we show that the neglecting of
the h* is not destructive yet for a nice correlation of the h*-constrained
entropic measure and its less demanding counterpart, which is much easier to
compute. Given examples illustrate a broad applicability of the measure and its
ability to quantify some of the subtleties of a fractional Brownian motion,
time evolution of a quasipattern [28,29] and reconstruction of a laser-speckle
pattern [2], which are hardly to discern or even missed.Comment: 17 pages, 5 figure