  We investigate the conditions under which the trace distance between two
different states of a given open system increases in time due to the
interaction with an environment, therefore signalling non-Markovianity. We find
that the finite-time difference in trace distance is bounded by two sharply
defined quantities that are strictly linked to the occurrence of
system-environment correlations created throughout their interaction and
affecting the subsequent evolution of the system. This allows to shed light on
the origin of non-Markovian behaviours in quantum dynamics. We best illustrate
our findings by tackling two physically relevant examples: a non-Markovian
dephasing mechanism that has been the focus of a recent experimental endeavour
and the open-system dynamics experienced by a spin connected to a finite-size
quantum spin chain.
