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

Abstract

This article deals with the molecular dynamics simulation of open systems that can exchange energy and matter with a reservoir; the physics of the reservoir and its interactions with the system are described by the model introduced by Bergmann and Lebowitz (P G Bergmann and J L Lebowitz 1955 Phys. Rev. http://dx.doi.org/10.1103/PhysRev.99.578 99 http://dx.doi.org/10.1103/PhysRev.99.578 ). Despite its conceptual appeal, the model did not gain popularity in the field 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 that mimic open systems. We shall demonstrate that the model can serve as a tool in devising both numerical procedures and conceptual definitions of physical quantities that cannot be defined in a straightforward way by systems with a fixed number of molecules. 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 resolution method (GC-AdResS) and report numerical results for the case of liquid water.

Keywords

• grand canonical
• Bergmann–Lebowitz Liouville equation
• adaptive resolution