Large deviation entropy defines the geometry of empirical data manifolds, breaking spherical geometry for pairwise statistics, and equates information projections from information geometry with those in Kolmogorov probability theory under i.i.d. and Markov assumptions.
More is different: Broken symmetry and the nature of the hierarchical structure of science
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The Geometry of Statistical Data and Information: A Large Deviation Perspective
Large deviation entropy defines the geometry of empirical data manifolds, breaking spherical geometry for pairwise statistics, and equates information projections from information geometry with those in Kolmogorov probability theory under i.i.d. and Markov assumptions.