  Information theoretic geometry near critical points in classical and quantum
systems is well understood for exactly solvable systems. Here we show that
renormalization group flow equations can be used to construct the information
metric and its associated quantities near criticality, for both classical and
quantum systems, in an universal manner. We study this metric in various cases
and establish its scaling properties in several generic examples. Scaling
relations on the parameter manifold involving scalar quantities are studied,
and scaling exponents are identified. The meaning of the scalar curvature and
the invariant geodesic distance in information geometry is established and
substantiated from a renormalization group perspective.
