  While originally discovered in the context of the Gaussian Unitary Ensemble,
the Tracy-Widom distribution also rules the height fluctuations of growth
processes. This suggests that there might be other nonequilibrium processes in
which the Tracy-Widom distribution plays an important role. In our contribution
we study one-dimensional systems with domain wall initial conditions. For an
appropriate choice of parameters the profile develops a rarefaction wave, while
maintaining the initial equilibrium states far to the left and right, which
thus serve as infinitely extended thermal reservoirs. For a Fermi-Pasta-Ulam
type anharmonic chain we will demonstrate that the time-integrated current has
a deterministic contribution, linear in time $t$, and fluctuations of size
$t^{1/3}$ with a Tracy-Widom distributed random amplitude.
