mappings for the new variables we propose 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 where the normalization factor N [ y ] is 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. 14 N [ y ] = ∫ D c Ω$_{1}$[ x ] exp ( − ∫ V d $^{3}$r λ ( r ) : Π [ c ]( r ) ) , (3.5c) ρ$_{(}$$_{Q,}$$_{q}$$_{)}$ [ c ] = Ω$_{1}$[ x ] N [ y ] exp ( − ∫ V d $^{3}$r λ ( r ) : Π [ c ]( r ) ) , (3.5b) ρ$_{y}$ [ x ] = δ (Π$_{ρ}$ − ρ ) δ ( Π$_{g}$ − g ) δ (Π$_{ϵ}$ − ϵ ) ρ$_{(}$$_{Q,}$$_{q}$$_{)}$ [ c ] , (3.5a) Π$_{P}$ [ c ]( r ) = ∫ V d $^{3}$r ′ |∇ c ( r $^{′}$) | 2 χ ( r − r $^{′}$) , (3.4a) Π$_{p}$ [ c ]( r ) = V d $^{3}$r ′ ( ( ∇ c ( r $^{′}$)) ( ∇ c ( r $^{′}$)) − 1 3 |∇ c ( r $^{′}$) | $^{2}$1 ) χ ( r − r $^{′}$) , (3.4b) Π$_{l}$[ c ]( r ) = ∫ V d $^{3}$r ′ |∇ c ( r $^{′}$) | χ ( r − r $^{′}$) V d $^{3}$r ′ |∇ c ( r $^{′}$) | 2 χ ( r − r $^{′}$) . (3.4c)