  Despite being ubiquitous, out-of-equilibrium quantum systems are much less
understood than systems at equilibrium. Progress in the field has benefited
from a symbiotic relationship between theoretical studies and new experiments
on coherent dynamics. The present work strengthens this connection by providing
a general picture of the relaxation process of isolated lattice many-body
quantum systems that are routinely studied in experiments with cold atoms, ions
traps, and nuclear magnetic resonance. We show numerically and analytically
that the long-time decay of the probability for finding the system in its
initial state necessarily shows a power-law behavior $\propto t^{ - \gamma }$.
This happens independently of the details of the system, such as integrability,
level repulsion, and the presence or absence of disorder. Information about the
spectrum, the structure of the initial state, and the number of particles that
interact simultaneously is contained in the value of $\gamma$. From it, we can
anticipate whether the initial state will or will not thermalize.
