  Irreversibility, despite being a necessary condition for thermalization,
still lacks a sound understanding in the context of isolated quantum many-body
systems. In this work we approach this question by studying the behavior of
generic many-body systems under imperfect effective time reversal, where the
imperfection is introduced as a perturbation of the many-body state at the
point of time reversal. Based on numerical simulations of the full quantum
dynamics we demonstrate that observable echos occurring in this setting decay
exponentially with a rate that is independent of the perturbation; hence, the
sensitivity to perturbations is intrinsic to the system meaning that the
dynamics is effectively irreversible.
