  The nonequilibrium dynamics of anharmonic chains is studied by imposing an
initial domain-wall state, in which the two half lattices are prepared in
equilibrium with distinct parameters. We analyse the Riemann problem for the
corresponding Euler equations and, in specific cases, compare with molecular
dynamics. Additionally, the fluctuations of time-integrated currents are
investigated. In analogy with the KPZ equation, their typical fluctuations
should be of size $t^{1/3}$ and have a Tracy-Widom GUE distributed amplitude.
The proper extension to anharmonic chains is explained and tested through
molecular dynamics. Our results are calibrated against the stochastic LeRoux
lattice gas.
