Complex soft matter systems can be efficiently studied with the help of adaptive resolution simulation
methods, concurrently employing two levels of resolution in different regions of the simulation
domain. The non-matching properties of high- and low-resolution models, however, lead to thermodynamic
imbalances between the system’s subdomains. Such inhomogeneities can be healed by
appropriate compensation forces, whose calculation requires nontrivial iterative procedures. In this
work we employ the recently developed Hamiltonian Adaptive Resolution Simulation method to
perform Monte Carlo simulations of a binary mixture, and propose an efficient scheme, based on
Kirkwood Thermodynamic Integration, to regulate the thermodynamic balance of multi-component
systems.