  We investigate the efficiency of a quantum Carnot engine based on open
quantum dynamics theory. The model includes time-dependent external fields for
the subsystems controlling the isothermal and isentropic processes and for the
system--bath (SB) interactions controlling the transition between these
processes. Numerical simulations are conducted in a nonperturbative and
non-Markovian SB coupling regime using the hierarchical equations of motion
under these fields at different cycle frequencies. The work applied to the
total system and the heat exchanged with the baths are rigorously evaluated. In
addition, by regarding quasi-static work as free energy, we compute the quantum
thermodynamic variables and analyze the simulation results using thermodynamic
work diagrams for the first time. Analysis of these diagrams indicates that, in
the strong SB coupling region, the fields for the SB interactions are major
sources of work, while in other regions, the field for the subsystem is a
source of work. We find that the maximum efficiency is achieved in the
quasi-static case and is determined solely by the bath temperatures, regardless
of the SB coupling strength, which is a numerical manifestation of Carnot's
theorem.
