Molecular dynamics in a grand ensemble: Bergmann–Lebowitz model and adaptive resolution simulation

This article deals with themolecular dynamics simulation of open systems that can exchange energy andmatter with a reservoir; the physics of the reservoir and its interactions with the system are described by themodel introduced by Bergmann and Lebowitz (PGBergmann and J L Lebowitz 1955 Phys. Rev. 99 578). Despite its conceptual appeal, themodel did not gain popularity in thefield of molecular simulation and, as a consequence, did not play a role in the development of open system molecular simulation techniques, even though it can provide the conceptual legitimation of simulation techniques thatmimic open systems.We shall demonstrate that themodel can serve as a tool in devising both numerical procedures and conceptual definitions of physical quantities that cannot be defined in a straightforwardway by systemswith afixed number ofmolecules. In particular, we discuss the utility of the Bergmann–Lebowitz (BL)model for the calculation of equilibrium time correlation functions within the grand canonical adaptive resolutionmethod (GC-AdResS) and report numerical results for the case of liquidwater.