Why Do Simple Models Work? Partial Answers from Information Geometry - Lecture 1

Explore the fundamental question of why simple models are effective in physics and biology through this lecture on information geometry. Delve into topics like thermodynamics of information processing, coding in statistical mechanics, and quantum information in extended systems. Examine concepts such as the renormalization group, information theory applications, and the emergence of useful parameters in complex systems. Follow along as the lecturer covers graph theory, nonlinear squares, coordinate transforms, microscopic models, eigenvectors, the Ising model, diffusion equations, and partition functions. Gain insights into how information theory and computational complexity characterize low-energy landscapes and govern physical behaviors like glassy phenomena. Suitable for advanced graduate students, post-docs, and junior researchers in statistical physics, biological physics, and quantum information theory.

US-India Advanced Studies Institute: Classical and Quantum Information
Why do simple models work? Partial answers from information geometry Lecture 1
Overview Slides ICTS Winter School: Classical and Quantum Information
Overview
Why do models work?
Why is physics comprehensible?
Outline for today
Graph
Calculate the metric again for nonlinear squares
Coordinate transform
Graphs
Reasonable microscopic model
Eigen vector corresponds to Eigen value
Two-dimensional Ising Model
Coordinate system
Diffusion equation
Partition function
Exercise
The Ising model after coarsening
Q&A