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The effect of microscopic correlations on the information geometric complexity of Gaussian statistical models

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  • Ali, S.A.
  • Cafaro, C.
  • Kim, D.-H.
  • Mancini, S.

Abstract

We present an analytical computation of the asymptotic temporal behavior of the information geometric complexity (IGC) of finite-dimensional Gaussian statistical manifolds in the presence of microcorrelations (correlations between microvariables). We observe a power law decay of the IGC at a rate determined by the correlation coefficient. It is found that microcorrelations lead to the emergence of an asymptotic information geometric compression of the statistical macrostates explored by the system at a faster rate than that observed in the absence of microcorrelations. This finding uncovers an important connection between (micro)correlations and (macro)complexity in Gaussian statistical dynamical systems.

Suggested Citation

  • Ali, S.A. & Cafaro, C. & Kim, D.-H. & Mancini, S., 2010. "The effect of microscopic correlations on the information geometric complexity of Gaussian statistical models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3117-3127.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:16:p:3117-3127
    DOI: 10.1016/j.physa.2010.03.028
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    References listed on IDEAS

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    1. Cafaro, C. & Ali, S.A., 2008. "Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6876-6894.
    2. Cafaro, Carlo, 2009. "Works on an information geometrodynamical approach to chaos," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 886-891.
    3. Lebowitz, Joel L., 1999. "Microscopic origins of irreversible macroscopic behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 516-527.
    4. Lebowitz, Joel L., 1993. "Macroscopic laws, microscopic dynamics, time's arrow and Boltzmann's entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 194(1), pages 1-27.
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    Cited by:

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    2. Gomez, Ignacio S. & Portesi, Mariela & Borges, Ernesto P., 2020. "Universality classes for the Fisher metric derived from relative group entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).

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