  The Toda chain with random initial data is studied. Of particular interest
are generalized Gibbs ensembles, their averaged conserved fields, and the
averages of the corresponding currents. While averaged fields are
well-understood, the description of averaged currents has hitherto relied on
the collision-rate assumption. For the Toda chain, the rate assumption can be
investigated numerically. Here, we provide convincing evidence for the validity
of the rate assumption. This lends further support to the idea that generalized
Euler-type equations have a structure common to all integrable extensive
systems.
