Role of chaos for the validity of statistical mechanics laws: diffusion and conduction

TL;DR

This paper investigates whether microscopic chaos is essential for the emergence of macroscopic diffusion and conduction phenomena in deterministic systems, addressing a fundamental question in statistical mechanics.

Contribution

It reexamines the role of deterministic chaos in the validity of statistical mechanics laws related to diffusion and heat conduction.

Findings

Chaos is not strictly necessary for diffusion and conduction.

Deterministic systems can exhibit macroscopic transport without microscopic chaos.

The study clarifies the conditions under which statistical laws hold in deterministic models.

Abstract

Several years after the pioneering work by Fermi Pasta and Ulam, fundamental questions about the link between dynamical and statistical properties remain still open in modern statistical mechanics. Particularly controversial is the role of deterministic chaos for the validity and consistency of statistical approaches. This contribution reexamines such a debated issue taking inspiration from the problem of diffusion and heat conduction in deterministic systems. Is microscopic chaos a necessary ingredient to observe such macroscopic phenomena?