Nonequilibrium thermodynamics for quantum systems strongly coupled to baths

Recent experimental advances in miniaturization of thermoelectric devices necessitate corresponding thermodynamic theory. Standard quantum thermodynamics (quantum statistical mechanics) assumes negligible system-bath coupling, but this assumption breaks down at nanoscale, where energy of the system is of the same order as the coupling. Thermodynamic formulation for nonequilibrium quantum systems strongly coupled to baths has not been fully developed yet. Several suggestions are available in recent literature. Here, we use a formulation utilizing von Neumann expression for reduced density matrix as system thermodynamic entropy to analyze the Carnot cycle in a nanoscale device. The formulation is the only one available today consistent with microscopic dynamics. We check consistency of the formulation by evaluating efficiency and entropy production of a single level model of the device coupled to macroscopic hot and cold fermionic reservoirs for weak (idealized) and strong (realistic) system-bath couplings at reversible driving. We show that lack of energy resolution in the formulation results in efficiency lower than the Carnot efficiency even at reversible driving and negative entropy production for some processes. To restore intuitively expected reversible behavior at adiabatic driving and consistency with the second law of thermodynamics, an energy-resolved thermodynamic formulation has to be developed.