Box-ball system (BBS) is a distinguished example of soliton cellular automaton in one dimension. Its integrability has been studied extensively from the viewpoint of quantum groups, Bethe ansatz, ultradiscretization and tropical geometry. In this talk I introduce the generalized Gibbs ensemble of BBS solitons and present several results related to thermodynamic Bethe ansatz and generalized hydrodynamics. They include exact solutions to the speed equation for solitons and the stationary current, a novel connection of the speed to a scaled period matrix of the tropical Riemann theta function, explicit description of the density plateaux that emerge from domain wall initial conditions and so forth. (Joint work with Grégoire Misguich and Vincent Pasquier.)
