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A novel information-geometrodynamical approach to chaotic dynamics (IGAC) oncurved statistical manifolds based on Entropic Dynamics (ED) is presented and anew definition of information geometrodynamical entropy (IGE) as a measure ofchaoticity is proposed. The general classical formalism is illustrated in arelatively simple example. It is shown that the hyperbolicity of anon-maximally symmetric 6N-dimensional statistical manifold M_{s} underlying anED Gaussian model describing an arbitrary system of 3N degrees of freedom leadsto linear information-geometric entropy growth and to exponential divergence ofthe Jacobi vector field intensity, quantum and classical features of chaosrespectively. An information-geometric analogue of the Zurek-Paz quantum chaoscriterion in the classical reversible limit is proposed. This analogy isillustrated applying the IGAC to a set of n-uncoupled three-dimensionalanisotropic inverted harmonic oscillators characterized by a Ohmic distributedfrequency spectrum.

Geometrodynamics of Information on Curved Statistical Manifolds and its Applications to Chaos