Statistics
Scientific paper
Dec 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010dmap.conf..194l&link_type=abstract
DARK MATTER IN ASTROPHYSICS AND PARTICLE PHYSICS . Proceedings of the 7th International Heidelberg Conference on Dark 2009 . Hel
Statistics
Nonextensive Statistics, Dark Matter, Dark Energy
Scientific paper
Nature appears non-local and nonlinear on all observable levels resulting in a large variety of complex phenomena in different scientific fields. In this situation the classical Boltzmann-Gibbs extensive thermo-statistics, applicable whenever microscopic interactions and memory are short ranged and the environment is a continuous and differentiable manifold, fails. We are dealing with systems generally subject to spatial or temporal non-local interactions, evolving in a non-Euclidean/multi-fractal space-time, making their behavior nonextensive. An appropriate generalization of the entropy functional yields upon entropy maximization naturally power-law distributions as manifestation of long-range interactions and correlations in the system, controlled by a single and physically interpretable parameter. Moreover, the nonextensive context is per se subject to entropy bifurcation, generating a tandem character of structures, where higher order stationary states of reduced entropy reside besides lower order stationary states of increased entropy. After reviewing the fundamental theoretical concepts of nonextensive statistics, we focus on the significance and present status with particular attention to the problem of dark matter density distributions in relaxed large scale astrophysical structures as well as the dark energy domain, associating dark energy with self-interacting scalar fields, subject to highest degree of correlations, and appearing as natural content within the nonextensive statistical landscape.
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