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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
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Information geometry and the renormalization group.
Reevu Maity1, Subhash Mahapatra1, Tapobrata Sarkar1
1Department of Physics, Indian Institute of Technology, Kanpur 208016, India.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 15, 2015
Summary
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.
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.
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