  Box-ball system (BBS) is a prominent example of integrable cellular automata
in one dimension connected to quantum groups, Bethe ansatz,
ultradiscretization, tropical geometry and so forth. In this paper we study the
generalized Gibbs ensemble of BBS soliton gas by thermodynamic Bethe ansatz and
generalized hydrodynamics. The results include the solution to the speed
equation for solitons, an intriguing connection of the effective speed with the
period matrix of the tropical Riemann theta function, an explicit description
of the density plateaux that emerge from domain wall initial conditions
including their diffusive corrections.
