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

We consider the relative configurational entropy per cell SΔ 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 SΔ 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 SΔ is also given.

[1]  Azeddine Beghdadi,et al.  ENTROPIC AND MULTIFRACTAL ANALYSIS OF DISORDERED MORPHOLOGIES , 1993 .

[2]  S. Torquato.  Microstructure characterization and bulk properties of disordered two-phase media , 1986 .

[3]  R. Piasecki,et al.  Effective conductivity in association with model structure and spatial inhomogeneity of polymer/carbon black composites , 1996, cond-mat/0204057.

[4]  Gemunu H. Gunaratne,et al.  CHARACTERIZATIONS OF NATURAL PATTERNS , 1998 .

[5]  B. Hambly.  Fractals, random shapes, and point fields , 1994 .

[6]  Homogeneity characterization of binary grain mixtures using a variance analysis of two-dimensional numerical fractions , 1995 .

[7]  R. Piasecki,et al.  Quantitative characterization of inhomogeneity in thin metallic films using Garncarek's method , 1994 .

[8]  J. Feder,et al.  Microstructural sensitivity of local porosity distributions , 1992 .

[9]  R. P. J. Wagensberg.  The maximum entropy principle and the nature of fractals , 1998, cond-mat/9804257.

[10]  Clinton De W Van Siclen.  INFORMATION ENTROPY OF COMPLEX STRUCTURES , 1997 .

[11]  S. Torquato.  Unified methodology to quantify the morphology and properties of inhomogeneous media , 1994 .

[12]  Local entropy characterization of correlated random microstructures , 1996, cond-mat/9611015.

[13]  Jones,et al.  An invariant measure of disorder in patterns. , 1995, Physical review letters.

[14]  S. Berthier,et al.  Percolation in random-Sierpiński carpets: A real space renormalization group approach , 1996 .

[15]  Azeddine Beghdadi,et al.  Entropic analysis of random morphologies , 1994 .

[16]  D. Stoyan,et al.  Fractals, random shapes and point fields : methods of geometrical statistics , 1996 .

[17]  Degree of heterogeneity of thermal field a method of evaluation , 1992 .

[18]  R. Piasecki,et al.  What is a physical measure of spatial inhomogeneity comparable to the mathematical approach , 1999, cond-mat/0005447.