Autonomous modular quantum systems: Contextual Jarzynski relations

For autonomous quantum systems with modular structure we demonstrate that the Jarzynski relation can be reinterpreted to apply even locally: For this purpose certain contexts have to be introduced by selecting the system of interest versus its environment. The respective energy exchange is then divided into heat and work based on a generalized definition of these notions. In this way we are able to identify functional parts of the environment as either heat or work sources, respectively. We investigate different combinations of these functional parts with respect to contextual Jarzynski relations. Our analytical results are confirmed by numerical investigations on small multipartite systems.