Overview

Entropy rigidity results across dynamics and geometry share a common structure: an entropy bound, followed by a classification of equality cases, leading to algebraic or geometric rigidity. Traditionally, these results rely on homogeneous dynamics, representation theory, or deep measure classification theorems.

This post presents a probabilistic entropy rigidity template based on high-dimensional probability. The central idea is simple:

Entropy bounds arise from concentration; rigidity follows from equality in sharp concentration inequalities.

This framework unifies flat, curved, and evolving geometries using diffusion and quadratic energy models.

Tags:

  • entropy rigidity
  • dynamical systems
  • high-dimensional probability
  • Ricci flow
  • concentration of measure
  • Burns Law


JTPMath categories:

  • Research Notes
  • Probability & Geometry
  • Dynamics summary: "A probabilistic template for entropy rigidity based on concentration inequalities, equality cases, and curvature-driven diffusion."