Recent theoretical progress on an information geometrodynamical approach to chaos

Abstract

In this paper, we report our latest research on a novel theoretical information-geometric framework suitable to characterize chaotic dynamical behavior of arbitrary complex systems on curved statistical manifolds. Specifically, an information-geometric analogue of the Zurek-Paz quantum chaos criterion of linear entropy growth and an information-geometric characterization of chaotic (integrable) energy level statistics of a quantum antiferromagnetic Ising spin chain in a tilted (transverse) external magnetic field are presented.