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We review some recent coarse-graining and multi-scale methods, but also putforward some new ideas for addressing such issues. We find that, if one isguided by nonequilibrium statistical mechanics and thermodynamics, it ispossible to design well-founded multi-scale modeling tools that can linkmicroscopic models with macroscopic constitutive equations. Such multi-scalemodeling tools benefit from recently proposed approaches for static coarsegraining which are mainly built on potentials of mean force. For dynamicalproperties, however, coarse-grained models need to account for dissipativeeffects that arise due to fast degrees of freedom that are eliminated in favorof the remaining slowly varying ones. The proper definition of the set of thestate variables, effectively representing the nonequilibrium states is thefirst key to the success of such an approach. Linking the microscopic modelwith a macroscopic model built on these slowly relaxing variables is the secondkey. We illustrate the new approach for a flowing, low-molecular polymer melt.

Multiscale Modeling and Coarse Graining of Polymer Dynamics: Simulations Guided by Statistical Beyond-Equilibrium Thermodynamics