  Given that the physical properties of polymeric liquids extend on a wide
range of lengthscales, it is computationally convenient to represent them by
coarse-grained (CG) descriptions at various granularities to investigate local
and global properties simultaneously. This paper addresses how modeling the
same system with mixed resolutions affects the consistency of the structural
and thermodynamic properties, and shows that it is possible to formally derive
interacting potentials that ensure consistency of the relevant physical
properties in the mixed resolution region with the corresponding atomistic
resolution simulations. The composition, temperature, and density dependences
of such Mixed Resolution Potentials (MRPs) are investigated. In the limit of
long polymer chains, where Markovian statistics is obeyed, the MRPs are
analytically solved and decay with characteristic scaling exponents that depend
on the mixture composition and CG resolution of the two components. Adopting
MRPs simplifies the structure of multi-resolution simulations while
quantitatively producing the structural and thermodynamical properties of the
related atomistic systems such as radial distribution function and pressure.
