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mappings for the new variables we propose 

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The next step in the coarse-graining procedure is the choice of the nonequilibrium en- semble. The natural choice is for it to be of the mixed ensemble due to the choice of the macroscopic variables [41]. Since the hydrodynamic fields are simply mapped from the Cahn-Hilliard to the Doi-Ohta level, the appropriate probability distribution function is of the generalized microcanonical type. For the configurational variables, on the other hand, we choose a generalized canonical ensemble with the corresponding Lagrange multipliers λ$_{Q}$ , λ$_{q}$ and λ$_{l}$ . The total probability measure ρ$_{y}$ [ x ] then takes the form 

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where the normalization factor N [ y ] is 

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and Ω$_{1}$[ x ] = exp ( S $^{(1)}$( x ) /k$_{B}$ ) . The projection operators Π$_{Q}$, Π$_{q}$ , and Π$_{l}$ are, for simplicity, denoted by Π in the above equations. The Lagrange multipliers λ$_{Q}$ , λ$_{q}$ , and λ$_{l}$ , denoted by λ , are determined by the values of the slow variables y = 〈 x 〉 where the average is performed according to (3.1). Their interpretation and the identification of the proper values for the situation of interest is difficult and requires dynamic material information [48, 49]. However, for the results presented in this paper, the exact form of the nonequilibrium ensemble will not be needed. 

