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Information geometry and the renormalization group.

Reevu Maity1, Subhash Mahapatra1, Tapobrata Sarkar1

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Summary
This summary is machine-generated.

Renormalization group flow equations universally construct information metrics near critical points in classical and quantum systems. This approach reveals scaling properties and clarifies geometric concepts like scalar curvature from a new perspective.

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Area of Science:

  • Physics
  • Information Theory
  • Statistical Mechanics

Background:

  • Information theoretic geometry is well-understood for exactly solvable critical systems.
  • A universal method for constructing information metrics near criticality is lacking for general classical and quantum systems.

Purpose of the Study:

  • To develop a universal method for constructing the information metric and associated quantities near critical points using renormalization group (RG) flow equations.
  • To establish the scaling properties of this metric and identify scaling exponents.
  • To interpret the physical meaning of scalar curvature and geodesic distance in information geometry from an RG perspective.

Main Methods:

  • Application of renormalization group (RG) flow equations to construct the information metric.
  • Analysis of the metric's scaling properties in various classical and quantum systems.
  • Investigation of scaling relations on the parameter manifold.

Main Results:

  • Demonstrated that RG flow equations universally construct the information metric near criticality.
  • Established the scaling properties of the information metric for generic systems.
  • Identified scaling exponents and clarified the physical meaning of scalar curvature and geodesic distance.

Conclusions:

  • RG flow provides a universal framework for information geometry near critical points.
  • The study offers a new perspective on understanding critical phenomena through the lens of information geometry.