Thermodynamic translational invariance in concurrent multiscale simulations of liquids

AdResS multi scale simulations of liquid systems allow for a free exchange of particles between regions, where their interactions are described by different models. The desired "model coexistence" is somewhat reminiscent of phase-coexistence. But while the latter describes heterogeneous systems with position-independent interactions, AdResS is meant to generate homogeneous systems with position-dependent interactions. Here we formulate the bulk equilibrium conditions for model coexistence, discuss the connection between the Hamiltonian H-AdResS scheme and widely used free energy methods based on the Kirkwood coupling parameter method of thermodynamic integration, and point out the relation between thermodynamic corrections in AdResS simulations and tail corrections for truncated long-range potentials. In particular, we use the analogy to derive expressions for the form of the correction profiles in narrow transition zones, which cannot be fully described by the local coupling parameter approximation. Finally, we illustrate how to treat transient mergers of small, diffusing all atom zones attached to reference particles in dynamic AdResS simulations without additional calibrations beyond the initial parameterization of the correction profile for individual all atom zones.