  The theoretical description of quantum dynamics in an intriguing way does not
necessarily imply the underlying dynamics is indeed intriguing. Here we show
how a known very interesting master equation with an always negative decay rate
[eternal non-Markovianity (ENM)] arises from simple stochastic Schr\"odinger
dynamics (random unitary dynamics). Equivalently, it may be seen as arising
from a mixture of Markov (semi-group) open system dynamics. Both these
approaches lead to a more general family of CPT maps, characterized by a point
within a parameter triangle. Our results show how ENM quantum dynamics can be
realised easily in the laboratory. Moreover, we find a quantum
time-continuously measured (quantum trajectory) realisation of the dynamics of
the ENM master equation based on unitary transformations and projective
measurements in an extended Hilbert space, guided by a classical Markov
process. Furthermore, a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL)
representation of the dynamics in an extended Hilbert space can be found, with
a remarkable property: there is no dynamics in the ancilla state. Finally,
analogous constructions for two qubits extend these results from
non-CP-divisible to non-P-divisible dynamics.
