Local and global approaches to the thermodynamics of pure decoherence processes in open quantum systems

Abstract: We study the nonequilibrium thermodynamics of pure decoherence processes in open quantum systems coupled to a thermal reservoir. We review various definitions of central quantities, such as internal energy, work, heat and entropy production, developed within local and global approaches to quantum thermodynamics. Within local approaches thermodynamic quantities only refer to the open system's degrees of freedom, while in the global approaches certain quantities are defined by referring explicitly to the reservoir degrees of freedom. Employing a microscopic, analytically solvable model, we perform a comparison of these two perspectives, revealing substantial differences in the thermodynamic quantities and in the formulations of the first and second law. The main reason for these discrepancies is the fact that the global approaches involve the system-reservoir interaction which exchanges a large amount of energy with the environment, while the average open system energy is constant in time because the dynamics represents pure decoherence and does not affect the open system populations.