Numerically accurate simulations of a quantum Carnot engine were conducted in a non-perturbative and non-Markovian system-bath (SB) coupling regime based on the open quantum dynamics theory. The model includes time-dependent external fields for the subsystems controlling the isothermal and isentropic processes (B(t)) and for the SB interactions controlling the transition between isothermal and isentropic processes (Ak(t) for k= 1 and 2). Numerical simulations were conducted using the hierarchical equations of motion (HEOM) under these fields at different cycle frequencies. The work done to the total system and the heat exchanged with the baths were rigorously evaluated, showing that the thermal efficiency approaches the Carnot limit under a quasi-static condition. By regarding quasi-static work as free energy, we compute conjugated thermodynamic variables (M(t) and Dk(t)) to analyze the simulation results using thermodynamic work diagrams for the first time. Analysis of these diagrams indicated that in a strong SB coupling region, the fields for the SB interaction 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 temperatures of the baths, regardless of the SB coupling strength, which is a numerical manifestation of Carnot's theorem.

Numerically "exact" simulations of a quantum Carnot cycle: Analysis using thermodynamic work diagrams

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