  We investigate the effects of localized integrability-breaking perturbations
on the large times dynamics of thermodynamic quantum and classical systems. In
particular, we suddenly activate an impurity which breaks the integrability of
an otherwise homogeneous system. We focus on the large times dynamics and on
the thermalization properties of the impurity, which is shown to have mere
perturbative effects even at infinite times, thus preventing thermalization.
This is in clear contrast with homogeneous integrability-breaking terms, which
display the prethermalization paradigm and are expected to eventually cause
thermalization, no matter the weakness of the integrability-breaking term.
Analytic quantitative results are obtained in the case where the bulk
Hamiltonian is free and the impurity interacting.
