On the partitioning of Energy and Entropy in Time-Dependent Open Quantum Systems

A unified framework is established for partitioning the Energy and the Entropy of time-dependent Open Quantum Systems. Our analysis sheds light on a long standing debate in quantum thermodynamics on how to partition the energy and entropy of strongly coupled and strongly driven open quantum systems in a manner consistent with the first, second, and third laws of thermodynamics. We identify the quantum mechanically consistent and experimentally meaningful partition as the one dictated by how the Hilbert space of the entire universe is partitioned between the open system and its environment. We arrive at this identification by critically examining the role of the reservoirs that make up the environment and that of the local interface between the system and its environment, thereby carefully accounting for heat in such systems. Fully general expressions for all thermodynamic quantities entering the first law, derived using Non-equilibrium Green's functions, are numerically implemented to perform a complete thermodynamic analysis of several open quantum machines that are driven in time both reversibly, and far from equilibrium. Finally, we perform an analysis of the spatio-temporal distribution and flow of the energy and entropy in these systems.