  We investigate the effect of different metrizations of probability spaces on
the information geometric complexity of entropic motion on curved statistical
manifolds. Specifically, we provide a comparative analysis based upon
Riemannian geometric properties and entropic dynamical features of a Gaussian
probability space where the two distinct dissimilarity measures between
probability distributions are the Fisher-Rao information metric and the
alpha-order entropy metric. In the former case, we observe an asymptotic linear
temporal growth of the information geometric entropy (IGE) together with a fast
convergence to the final state of the system. In the latter case, instead, we
note an asymptotic logarithmic temporal growth of the IGE together with a slow
convergence to the final state of the system. Finally, motivated by our
findings, we provide some insights on a tradeoff between complexity and speed
of convergence to the final state in our information geometric approach to
problems of entropic inference.
