for closed systems and it drives the reversible dynamics. Therefore, for the irreversible dynamics the entropy presents an important quantity — it does not decrease for closed systems. For the GENERIC formulation, it is then assumed that the irreversible contribution to the time evolution, ˙ x |$_{irrev}$ , is driven by the entropy gradient, i.e., that it is of the form ˙ x |$_{irrev}$ = M · ( δS/δ x ), with M a generalized friction matrix. This friction matrix contains transport coefficients and relaxation times associated to the corresponding dissipative effects. It is required for M to be (Onsager-Casimir) symmetric and the condition that it is positive semi-definite ensures that ˙ S ≥ 0 is fulfilled. From the above illustration, one concludes that the time evolution of x can be expressed in terms of four “building blocks” E , S , L and M as The two different contributions to the time evolution, reversible and irreversible, are not independent. They are related by the two complementary degeneracy requirements The first requirement expresses the reversible nature of the L contribution to the dynamics, demonstrating the fact that the reversible dynamics captured in L does not affect the entropy functional. The second one expresses the conservation of the total energy of an isolated system by the irreversible contribution to the system dynamics captured in M . The presented GENERIC form of the time evolution equations for the state variables x represents a mathematical structure which guarantees that the chosen model is thermody- namically consistent. Moreover, by concentrating on the thermodynamics building blocks E , S , L and M rather than on the time evolution equations in systematic coarse-graining pro- cedures, the obtained coarse-grained equations are guaranteed to be also thermodynamically admissible. In order to develop a systematic coarse-graining procedure which relates the more detailed Cahn-Hilliard level to the more macroscopic Doi-Ohta level, we must formulate the first one in the GENERIC structure. As a first step, we need to identify the list of independent A. GENERIC formulation of the Cahn-Hilliard model 7 ˙ x = L ( x ) · δE ( x ) δ x + M ( x ) · δS ( x ) δ x . (2.2) L ( x ) · δS ( x ) δ x = 0 , M ( x ) · δE ( x ) δ x = 0 . (2.3)