  We study a one-dimensional gas of hard rods trapped in a harmonic potential,
which breaks integrability of the hard-rod interaction in a non-uniform way. We
explore the consequences of such broken integrability for the dynamics of a
large number of particles and find three distinct regimes: initial, chaotic,
and stationary. The initial regime is captured by an evolution equation for the
phase-space distribution function. For any finite number of particles, this
hydrodynamics breaks down and the dynamics become chaotic after a
characteristic time scale determined by the inter-particle distance and
scattering length. The system fails to thermalize over the time-scale studied
($10^4$ natural units), but the time-averaged ensemble is a stationary state of
the hydrodynamic evolution. We close by discussing logical extensions of the
results to similar systems of quantum particles.
