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We introduce the complete box-ball system (cBBS), which is an integrablecellular automaton on 1D lattice associated with the quantum group$U_q(\widehat{sl}_n)$. Compared with the conventional $(n-1)$-color BBS, itenjoys a remarkable simplification that scattering of solitons is totallydiagonal. We also submit the cBBS to randomized initial conditions and studyits non-equilibrium behavior by thermodynamic Bethe ansatz and generalizedhydrodynamics. Excellent agreement is demonstrated between theoreticalpredictions and numerical simulation on the density plateaux generated fromdomain wall initial conditions including their diffusive broadening.

Generalized hydrodynamics in complete box-ball system for $U_q(\widehat{sl}_n)$