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We characterize the complexity of geodesic paths on a curved statisticalmanifold M_{s} through the asymptotic computation of the information geometriccomplexity V_{M_{s}} and the Jacobi vector field intensity J_{M_{s}}. Themanifold M_{s} is a 2l-dimensional Gaussian model reproduced by an appropriateembedding in a larger 4l-dimensional Gaussian manifold and endowed with aFisher-Rao information metric g_{{\mu}{\nu}}({\Theta}) with non-trivial offdiagonal terms. These terms emerge due to the presence of a correlationalstructure (embedding constraints) among the statistical variables on the largermanifold and are characterized by macroscopic correlational coefficients r_{k}.First, we observe a power law decay of the information geometric complexity ata rate determined by the coefficients r_{k} and conclude that the non-trivialoff diagonal terms lead to the emergence of an asymptotic information geometriccompression of the explored macrostates {\Theta} on M_{s}. Finally, we observethat the presence of such embedding constraints leads to an attenuation of theasymptotic exponential divergence of the Jacobi vector field intensity.

Quantifying The Complexity Of Geodesic Paths On Curved Statistical Manifolds Through Information Geometric Entropies and Jacobi Fields