Bridging scales is viewed in this contribution from the perspective of nonequilibrium thermodynamics, particularly using the framework known as the “general equation for the nonequilibrium reversible-irreversible coupling” (GENERIC). This framework is a generalization of Ginzburg-Landau-type dynamics, i.e. the dynamics is understood as being driven by derivatives of thermodynamic potentials, and the relaxation to equilibrium is governed by kinetic coefficients.

It is shown that this framework offers the tools to tackle two major issues in multiscale modeling. First, multiscale models suitable for transient situations can be devised in which the variables on the different levels of description communicate concurrently, i.e. are coupled mutually at every moment in time. This is illustrated with specific examples from complex fluids and solid mechanics.

The second major achievement of the GENERIC framework, which will be discussed in detail, is that it provides an explicit tool for systematic coarse-graining, which involves statistical mechanics procedures and projection operator methods. On the one hand, statistical mechanics of extended canonical ensembles is employed to determine the thermodynamic potentials, the derivatives of which are needed to drive the dynamics of the coarse-grained model. On the other hand, projection operator techniques are employed to split the dynamics into two contributions, namely into what is under mechanistic control on the coarse-grained scale and the rest, i.e. the fluctuations. The latter must not be simply averaged out during coarse-graining, but rather their time-correlation functions give rise to (irreversible) kinetic coefficients in the coarse grained model. Examples from complex fluids and solid mechanics are employed to demonstrate the practical usefulness of systematic coarse graining. Finally, it is discussed why the separation of time scales is essential for understanding the emergence of irreversibility upon coarse-graining.