we have minimum and maximum translational entropy loss respectively. We should note that there are complicated competitive terms in the Hamiltonian between non-bonded interaction and the entropic term which are captured by free energy minimization. The translational entropy term, $Q\left[ i w\right]$ is the only term which represents the connectivity of the polymers, therefore the spatial non-locality only arises from this term which indicates in confined geometry, we have to apply the boundary conditions to the propagator of a single-chain and geometrical boundary condition has nothing to do with other terms in the effective Hamiltonian [@Glenn]. We can conclude that in confined geometries, the entropic term is the dominant factor which tries to minimize the free energy of the system.

Multiple similar chains; no segregation
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![(color online) monomer number density for homogeneous systems. (a) long segment polymers (b) short segment polymers. For homogeneous system where all the chains are homopolymers, there is no competition between the chains and both short and long segment chains behave similarly. The fluctuation (oscillation) close to the boundary resembles the solvation force and liquid layering adjacent to the solid surface where we can distinguish the contact and midpoint densities. The surface forces the monomers 