Thermodynamics of small quantum systems and small environments

With the rapid development of quantum technologies and the ability to manipulate individual atoms and ion, thermodynamics faces new challenges. The main question is not whether thermodynamics is valid, but whether it is relevant. Does it provide useful predictions on quantities of interest in the microscopic world? By introducing the concept of global passivity we derive an extension of the second law of thermodynamics that can properly handle initial  quantum correlations (i.e., entanglement, and quantum discord) between the system and the environment. This extension is very important in nanoscopic setups where the environment may be small and strongly interacting with the system of interest. A second main finding of this framework is a family of additional thermodynamic relations that involve measurable quantities that were so far not constrained by thermodynamics. In particular, we use these relations to set upper and lower bounds on the buildup of system-environment correlation in quantum dephasing scenarios (decoherence). As a second example, we study the evolution of energy covariance between an atom and an optical cavity. Our findings are highly relevant for various modern experimental setups such as ion traps, atoms in an optical cavity or in optical lattices, and more.