Giorgilli: it The Fermi–Pasta–Ulam problem as a challenge for the foundations of physics, Chaos 15

The FPU problem is discussed in connection with its physical relevance, and it is shown how apparently there exist only two possibilities: either the FPU problem is just a curiosity, or it has a fundamental role for the foundations of physics, casting a new light on the relations between classical and quantum mechanics. To this end, a short review is given of the main conceptual proposals that have been advanced. Particular emphasis is given to the perspective of a metaequilibrium scenario, which appears to be the only possible one for the FPU paradox to survive in the physically relevant case of infinitely many particles. Key words: FPU problem, relaxation times, metaequilibrium PACS: 05.20.–y No doubt, the FPU problem (see [1] and the review [2]) did play a relevant role in the theory of dynamical systems. Indeed, first of all, with the works of Zabusky and Kruskal it prompted the modern theories of solitons and of infinitely–dimensional integrable systems