  The adaptive resolution simulation (AdResS) technique couples regions with
different molecular resolutions and allows the exchange of molecules between
different regions in an adaptive fashion. The latest development of the
technique allows to abruptly couple the atomistically resolved region with a
region of non-interacting point-like particles. The abrupt set-up was derived
having in mind the idea of the atomistically resolved region as an open system
embedded in a large reservoir at a given macroscopic state. In this work,
starting from the idea of open system, we derive thermodynamic relations for
AdResS which justify conceptually and numerically the claim of AdResS as a
technique for simulating open systems. In particular, we derive the relation
between the chemical potential of the AdResS set-up and that of its reference
fully atomistic simulation. The implication of this result is that the grand
potential of AdResS can be explicitly written and thus, from a statistical
mechanics point of view, the atomistically resolved region of AdResS can be
identified with a well defined open system.
