Journal of Statistical Physics, Vol. 52, Nos. 1/2, 1988. p. 497-502.
This note concerns the long-time behavior of a one-dimensional mechanical system, hard rods with equal masses and lengths interacting by elastic collisions. We have noticed that for much longer times than those at
which the Euler equation is valid macroscopic observables develop stochastic behavior; this might be contrasted with the expected picture based on the description of the long-time behavior of the system in terms of a Navier-Stokes correction to the Euler equation. We propose a scheme for defining an operator reminiscent of the wave operator and of the Mo11er morphism in scattering theory, which could be considered in one case as defining the Navier-Stokes correction while still being meaningful when the Navier-Stokes description fails...