  The Toda chain is the prime example of a classical integrable system with
strictly local conservation laws. Relying on the Dumitriu-Edelman matrix model,
we obtain the generalized free energy of the Toda chain and thereby establish a
mapping to the one-dimensional log-gas with an interaction strength of order
1/N. The (deterministic) local density of states of the Lax matrix is
identified as the object, which should evolve according to generalized
hydrodynamics. In the current version missing factors of 2 are corrected.
