Irreversibility and Dissipation Through Coarse Graining

The fact that we do not account explicitly for the irrelevant variables at the level of the GENERIC framework leads to entropy increase and additional dissipation at the coarser level of description [11]. 

The coarse-grained entropy plays the role of an effective potential for the relevant variables. Determining the functional form of S(x) from (7.9) presents a challenge since the explicit expression for the Lagrange multipliers Aj (x) is in general unknown. A successful method for extracting at least partial information on S(x) has been explored in Ref [164] from atomistic simulations of a polymer melt in elongational flow. We discuss this issue further in Sections 7.4.2 and 7.4.3. 

The separating timescale Ts should be chosen large enough to comprise all the fast fluctuations that are not captured on the coarse-grained level [167]. Thus, the friction matrix M arises due to fast fluctuations that are not resolved at the coarser level. The numerical evaluation of the dissipation matrix (7.10) for a polymer melt is described in Section 7.4.3. 

Thermodynamically Cuided Coarse-Crained Polymer Simulations Beyond Equilibrium 

CENERIC Coarse-Craining Applied to Unentangled Melts Foundations 

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