Generalized Gibbs Ensembles of the classical Toda chain

Understand

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.