Entropic descriptor of a complex behaviour

We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system’s entropy S from both its maximum possible value Smax and its minimum possible value Smin. When these two departures are similar to each other, the statistical complexity is maximal. We apply the new concept to the variability, over a range of length scales, of spatial or grey-level pattern arrangements in simple models. The pertinent results confirm the fact that a highly non-trivial, length scale dependence of the entropic descriptor makes it an adequate complexity measure, able to distinguish between structurally distinct configurational macrostates with the same degree of disorder, a feature that makes it a good tool for discerning structures in complex patterns.

[1]  Matt Davison,et al.  Extended Entropies and Disorder , 2005, Adv. Complex Syst..

[2]  P. Landsberg,et al.  Simple measure for complexity , 1999 .

[3]  Osvaldo A. Rosso,et al.  Intensive entropic non-triviality measure , 2004 .

[4]  David R Poirier,et al.  The mechanical properties of thermite welds in premium alloy rails , 1984 .

[5]  Salvatore Torquato,et al.  Pair Correlation Function Realizability: Lattice Model Implications † , 2004 .

[6]  Daniel F. Styer,et al.  Insight into entropy , 2000 .

[7]  Edoardo Patelli,et al.  On optimization techniques to reconstruct microstructures of random heterogeneous media , 2009 .

[8]  Ryszard Piasecki.  Statistical mechanics characterization of spatio-compositional inhomogeneity , 2009 .

[9]  R. Stanley.  What Is Enumerative Combinatorics , 1986 .

[10]  Ryszard Piasecki.  Detecting self-similarity in surface microstructures , 2000 .

[11]  F. Stillinger,et al.  Modeling heterogeneous materials via two-point correlation functions. II. Algorithmic details and applications. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  R. Piasecki.  A versatile entropic measure of grey level inhomogeneity , 2009 .

[13]  Ryszard Piasecki.  Entropic measure of spatial disorder for systems of finite-sized objects , 2000 .

[14]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[15]  A. Vulpiani,et al.  Predictability: a way to characterize complexity , 2001, nlin/0101029.

[16]  Salvatore Torquato,et al.  Microstructure functions for a model of statistically inhomogeneous random media , 1997 .

[17]  N. Pan,et al.  Predictions of effective physical properties of complex multiphase materials , 2008 .

[18]  Young,et al.  Inferring statistical complexity. , 1989, Physical review letters.

[19]  S. Torquato.  Random Heterogeneous Materials , 2002 .

[20]  Carl S. McTague,et al.  The organization of intrinsic computation: complexity-entropy diagrams and the diversity of natural information processing. , 2008, Chaos.

[21]  Binder,et al.  Comment II on "Simple measure for complexity" , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[22]  Gianpietro Malescio,et al.  Stripe phases from isotropic repulsive interactions , 2003, Nature materials.

[23]  R. Stoop,et al.  Shiner–Davison–Landsberg complexity revisited , 2005 .

[24]  Leonid A. Bunimovich,et al.  Complexity of Dynamics as Variability of Predictability , 2004 .

[25]  Shiner,et al.  Reply to comments on "Simple measure for complexity" , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Nonadditive statistical measure of complexity and values of the entropic index q , 2004, cond-mat/0402217.

[27]  S. Torquato,et al.  Reconstructing random media , 1998 .

[28]  Crutchfield,et al.  Comment I on "Simple measure for complexity" , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[29]  R. Piasecki.  A generalization of the inhomogeneity measure for point distributions to the case of finite size objects , 2006, cond-mat/0612401.

[30]  Duality and spatial inhomogeneity , 2001, cond-mat/0107604.

[31]  Osvaldo A. Rosso,et al.  Generalized statistical complexity measures: Geometrical and analytical properties , 2006 .

[32]  C. Tsallis.  Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World , 2009 .

[33]  Eckehard Olbrich,et al.  How should complexity scale with system size? , 2008 .

[34]  Osvaldo A. Rosso,et al.  Statistical complexity and disequilibrium , 2003 .

[35]  Celia Anteneodo,et al.  Some features of the López-Ruiz-Mancini-Calbet (LMC) statistical measure of complexity , 1996 .

[36]  J. Crutchfield,et al.  Measures of statistical complexity: Why? , 1998 .

[37]  Ricardo López-Ruiz,et al.  A Statistical Measure of Complexity , 1995, ArXiv.

[38]  R. Piasecki,et al.  Inhomogeneity and complexity measures for spatial patterns , 2002 .