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. 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.
Highlights
The physics of open systems is considered to be of primary importance in the understanding of natural phenomena and in the development of modern technology [1]
From a theoretical point of view the conceptual development of the classical and quantum statistical mechanics of open systems is challenging; theorems of statistical mechanics and dynamics derived for systems with a fixed number of particles are no longer valid in their standard formulation and must be revised e.g., if the deterministic evolution is substituted with the stochastic evolution which controls the process of exchange of particles [3,4,5,6,7]
Recently algorithms of multiscale character, which aim at bridging different scales within one unified framework, have gained great popularity, which in turn has led to the construction of efficient techniques where systems exchange energy or particles with an external environment; for example techniques using molecular resolution that can adaptively change in space, see e.g. [9] and [10] and references therein
Summary
The physics of open systems is considered to be of primary importance in the understanding of natural phenomena and in the development of modern technology [1]. In contrast to the first generation of algorithms with a varying number of particles, such algorithms are technically highly efficient and flexible This flexibility makes them feasible for use in the calculation of various statistical properties, such as time correlation functions, some of which require a theoretical redefinition (compared to the fixed particle number simulations). The aim of this paper is: (a) a discussion of theoretical concepts of open systems present in the literature; (b) a brief overview about the development/ application of algorithms with a varying number of particles in molecular dynamics; (c) the inclusion/ adaptation of formal results about open systems into the framework of MD techniques; (d) to provide examples of merging theory and algorithms by reporting numerical results for one specific open system MD technique. The results show that, with the technical setup developed in this work, the method is reliable for the calculation of static properties, on which past research focused, and for the calculation of dynamical properties, allowing the study of a much larger class of phenomena
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