Origins of Diffusion

TL;DR

This paper studies a lattice-based dynamical system with hyperbolic subsystems and conserved energy, demonstrating that the long-term energy distribution evolves diffusively.

Contribution

It proves that weak coupling among hyperbolic subsystems leads to diffusive energy dynamics over time.

Findings

Subsystem energies exhibit diffusive behavior over long times

Conservation of total energy is maintained

Diffusion is rigorously proven for the model

Abstract

We consider a dynamical system consisting of subsystems indexed by a lattice. Each subsystem has one conserved degree of freedom ("energy") the rest being uniformly hyperbolic. The subsystems are weakly coupled together so that the sum of the subsystem energies remains conserved. We prove that the long time dynamics of the subsystem energies is diffusive.