Originally conceived exclusively for macroscopic classical devices close to equilibrium, the laws of thermodynamics were shown during the last decades to actually hold for microscopic individual systems, both classical or quantum, arbitrarily far from equilibrium and the so-called thermodynamic limit. Despite constituting a giant’s step, these results are so far established  for ideal sources of work (i.e. external field described classically) and pure sources of heat (quantum systems at thermal equilibrium). In contrast, recent studies demonstrated that realistic quantum machines generically involve hybrid work/heat sources, which do not fit in this picture. In addition, one can wonder if it is possible to define heat and work exchanges between two (or more) arbitrary quantum systems, and see the emergence of the laws of thermodynamics in an autonomous, fully quantum, formalism. Here, we start from an extension of the previously known expression of the second law for quantum systems to provide generalized notions of the work and heat exchanged between arbitrary autonomous quantum systems. Our definitions comply with the usual laws of thermodynamics, which then lead to identifying the resources that can be consumed to decrease entropy (or revert the direction of a heat flow) at the nanoscale. We envision two types of applications: First, we design microscopic machines where work and heat sources are all played by elementary quantum systems, such as a refrigerator solely composed of two qubits. Second, we are able to analyze situations leading to exchange work with a large system initially at equilibrium and therefore traditionally considered as a heat bath. This is illustrated on the spin-boson model by a quantum dynamo effect, i.e. a work-to-work conversion mediated by dissipation.

Contact : Dragi Karevski