  Nonequilibrium dynamics of a nonintegrable system without the eigenstate
thermalization hypothesis is studied. It is shown that, in the thermodynamic
limit, this model thermalizes after an arbitrary quantum quench at finite
temperature, although it does not satisfy the eigenstate thermalization
hypothesis. In contrast, when the system size is finite and the temperature is
low enough, the system may not thermalize. In this case, the steady state is
well described by the generalized Gibbs ensemble constructed by using highly
nonlocal conserved quantities. We also show that this model exhibits
prethermalization, in which the prethermalized state is characterized by
nonthermal energy eigenstates.
