Collision rate ansatz for the classical Toda lattice.

We consider a generalized Gibbs ensemble of the classical Toda lattice. We establish that the collision rate ansatz follows because (i) the charge-current susceptibility matrix is symmetric and (ii) the stretch current is proportional to the momentum, hence conserved. The method applies also to other integrable many-body systems, either classical or quantum, provided there is a self-conserved current.