The Effect Of Microscopic Correlations On The Information Geometric Complexity Of Gaussian Statistical Models
arXiv:1005.2292 · doi:10.1016/j.physa.2010.03.028
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 absence of microcorrelations. This finding uncovers an important connection between (micro)-correlations and (macro)-complexity in Gaussian statistical dynamical systems.
12 pages; article in press, Physica A (2010).
References in corpus (10)
- Updating Probabilities
- Chaos and Complexity of quantum motion
- Entropic Dynamics
- Jacobi Fields on Statistical Manifolds of Negative Curvature
- How complex is the quantum motion?
- Works on an information geometrodynamical approach to chaos
- Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?
- Information Geometry, Inference Methods and Chaotic Energy Levels Statistics
- Information-Geometric Indicators of Chaos in Gaussian Models on Statistical Manifolds of Negative Ricci Curvature
- Quantum information science as an approach to complex quantum systems
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