  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?
