  We study a limit cycle of a quantum Otto engine whose each cycle consists of
two finite-time quantum isochoric (heating or cooling) processes and two
quantum adiabatic work-extracting processes. Considering a two-level system as
a working substance that weakly interacts with two reservoirs comprising an
infinite number of bosons, we investigate the non-Markovian effect (short-time
behavior of the reduced dynamics in the quantum isochoric processes (QIPs)) on
work extraction after infinite repetition of the cycles. We focus on the
parameter region where energy transferred to the reservoir can come back to the
system in a short-time regime, which we call energy backflow to show partial
quantum-mechanical reversibility. As a situation completely different from
macroscopic thermodynamics, we find that the interaction energy is finite and
negative by evaluating the average energy change of the reservoir during the
QIPs by means of the full-counting statistics, corresponding to the two-point
measurements. The feature leads us to the following findings: (1) the Carnot
theorem is consistent with a definition of work including the interaction
energy, although the commonly used definition of work excluding the interaction
leads to a serious conflict with the thermodynamic law, and (2) the energy
backflow can increase the work extraction. Our findings show that we need to
pay attention to the interaction energy in designing a quantum Otto engine
operated in a finite time, which requires us to include the non-Markovian
effect, even when the system-reservoir interaction is weak.
