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

TL;DR

This paper presents numerically exact simulations of a quantum Carnot cycle, analyzing efficiency and work using thermodynamic diagrams in a nonperturbative, non-Markovian regime, confirming Carnot's theorem in quantum thermodynamics.

Contribution

It introduces a novel analysis of quantum Carnot cycles using thermodynamic work diagrams in a nonperturbative, non-Markovian framework, revealing the roles of different fields in work extraction.

Findings

Maximum efficiency occurs in the quasi-static limit, determined solely by bath temperatures.

Fields controlling system-bath interactions are major work sources in strong coupling regimes.

Efficiency aligns with classical Carnot limits regardless of coupling strength.

Abstract

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.