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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. Weexplore the consequences of such broken integrability for the dynamics of alarge number of particles and find three distinct regimes: initial, chaotic,and stationary. The initial regime is captured by an evolution equation for thephase-space distribution function. For any finite number of particles, thishydrodynamics breaks down and the dynamics become chaotic after acharacteristic time scale determined by the inter-particle distance andscattering length. The system fails to thermalize over the time-scale studied($10^4$ natural units), but the time-averaged ensemble is a stationary state ofthe hydrodynamic evolution. We close by discussing logical extensions of theresults to similar systems of quantum particles.

Incomplete thermalization from trap-induced integrability breaking: lessons from classical hard rods