  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.
