title: Information geometry and the renormalization group.
abstract: 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 a 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.
authors.affiliation: Department of Physics, Indian Institute of Technology, Kanpur 208016, India.
authors.forename: Reevu
authors.initials: R
authors.lastname: Maity
authors.affiliation: Department of Physics, Indian Institute of Technology, Kanpur 208016, India.
authors.forename: Subhash
authors.initials: S
authors.lastname: Mahapatra
authors.affiliation: Department of Physics, Indian Institute of Technology, Kanpur 208016, India.
authors.forename: Tapobrata
authors.initials: T
authors.lastname: Sarkar