Coarse-grained modeling, coarse-grained models, aim at simulating the behaviour of complex systems using their coarse-grained (simplified) representation. Coarse-grained models are widely used for molecular modeling of biomolecules at various granularity levels. The Liouville theorem (sometimes also called Liouville equation) where Then,by maximisation for a given energy , i.e. linking with of the other sum equal to zero via a Lagrange multiplier , one obtains (as in the case of a lattice of spins or with a bit at each lattice point) and , Then in terms of ensemble averages , and