Entropic measure of spatial disorder for systems of finite-sized objects

Abstract

We consider the relative configurational entropy per cell S_Delta as a measure of the degree of spatial disorder for systems of finite-sized objects. It is highly sensitive to deviations from the most spatially ordered reference configuration of the objects. When applied to a given binary image it provides the quantitatively correct results in comparison to its point object version. On examples of simple cluster configurations, two-dimensional Sierpinski carpets and population of interacting particles, the behaviour of S_Delta is compared with the normalized information entropy H' introduced by Van Siclen [Phys. Rev. E 56, (1997) 5211]. For the latter example, the additional middle-scale features revealed by our measure may indicate for the traces of self-similar structure of the weakly ramified clusters. In the thermodynamic limit, the formula for S_Delta is also given.