  Nonintegrability plays a crucial role in thermalization and transport
processes in many-body Hamiltonian systems, yet its quantitative effects remain
unclear. To reveal the connection between the macroscopic relaxation properties
and the underlying dynamics, the one-dimensional diatomic hard-point model as
an illustrating example was studied analytically and numerically. We
demonstrate how the system transitions from kinetic behavior to hydrodynamic
behavior as the nonintegrability strength increases. Specifically, for the
thermalization dynamics, we find a power-law relationship between the
thermalization time and the perturbation strength near integrable regime,
whereas in the far from integrable regime, the hydrodynamics dominates and the
thermalization time becomes independent of the perturbation strength and
exhibits a strong size-dependent behavior. Regarding transport behavior, our
results further establish a threshold for the nonintegrable strength of this
transition. Consequently, we can predict which behavior dominates the transport
properties of the system. Especially, an explicit expression of the thermal
conductivity contributed by the kinetics is given. Finally, possible
applications were briefly discussed.
