The Effect Of Microscopic Correlations On The Information Geometric Complexity Of Gaussian Statistical Models

Details The Effect Of Microscopic Correlations On The Information Geometric Complexity Of Gaussian Statistical Models The Effect Of Microscopic Correlations On The Information Geometric Complexity Of Gaussian Statistical Models

2010-05-13

arxiv.org/abs/1005.2292v1

Physica A389, 3117 (2010)

Physics

Mathematical Physics

12 pages; article in press, Physica A (2010).

Scientific paper

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 absence of microcorrelations. This finding uncovers an important connection between (micro)-correlations and (macro)-complexity in Gaussian statistical dynamical systems.

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