  We demonstrate that the efficiency of effective negative temperature-based
quantum Otto engines, already known to outperform their traditional
counterparts operating with positive-temperature thermal reservoirs, can be
further improved by terminating the isochoric strokes before the working
substance reaches perfect equilibrium with its environment. Our investigation
encompasses both Markovian and non-Markovian dynamics during these finite-time
isochoric processes while considering a weak coupling between the working
substance and the reservoirs. We assess the performance of these engines as
they undergo a transition from the Markovian to the non-Markovian regime using
two figures of merit: maximum achievable efficiency at a certain finite time
during the isochoric heating stroke, and overall performance of the engine over
an extended period during the transient phase of this stroke. We show that the
maximum efficiency increases with the increase of non-Markovianity. However,
the overall engine performance decreases as non-Markovianity increases.
Additionally, we discover the existence of effective negative temperature-based
necessarily transient quantum Otto engines. These engines operate within an
extended operational domain, reaching into temperature ranges where
conventional effective negative temperature-based quantum Otto engines, which
rely on perfect thermalization during the isochoric strokes, are unable to
function. Furthermore, this extended operational domain of an effective
negative temperature-based necessarily transient quantum Otto engine increases
as non-Markovianity becomes more pronounced.
