  After a quench in a quantum many-body system, expectation values tend to
relax towards long-time averages. However, in any finite-size system, temporal
fluctuations remain. It is crucial to study the suppression of these
fluctuations with system size. The particularly important case of
non-integrable models has been addressed so far only by numerics and
conjectures based on analytical bounds. In this work, we are able to derive
analytical predictions for the temporal fluctuations in a non-integrable model
(the transverse Ising chain with extra terms). Our results are based on
identifying a dynamical regime of 'many-particle dephasing', where
quasiparticles do not yet relax but fluctuations are nonetheless suppressed
exponentially by weak integrability breaking.
