Finally, with the help of the mappings (3.4), we can recognize the appropriate terms in the last equation, so that their ensemble average gives L (2) P g $_{,β}$( r$_{1}$ , r$_{2}$ ) = ∂ ∂r$_{2}$$_{α}$ [( 2 p$_{αβ}$ ( r$_{2}$ ) − 1 3 P ( r$_{2}$ ) δ$_{αβ}$ ) χ ( r$_{1}$ − r$_{2}$ ) ] + P ( r$_{2}$ ) ∂χ ( r$_{1}$ − r$_{2}$ ) ∂r$_{2}$$_{β}$ . (A5) The Poisson operator element L (2) l g ( r$_{1}$ , r$_{2}$ ) is obtained under similar approximations as above, but also the following approximations ∫ V d $^{3}$r ′ $_{1}$Φ[ c ]( r ′ $_{1}$) χ ( r$_{1}$ − r ′ $_{1}$) χ ( r ′ 1 − r ′ $_{2}$) ≈ Φ[ c ]( r$_{1}$ ) χ ( r$_{1}$ − r ′ $_{2}$) , (A6) which holds under the assumption of the difference in length scales (3.2), and the assumption 〈 (Π$_{P}$ [ c ]( r )) $^{n}$Π$_{l}$ [ c ]( r ) 〉 ≈ ( 〈 Π$_{P}$ [ c ]( r ) 〉 ) n 〈 Π$_{l}$[ c ]( r ) 〉 , (A7) for n = ± 1. For the element L (2) l g ( r$_{1}$ , r$_{2}$ ), we then obtain L (2) l g $_{,β}$( r$_{1}$ , r$_{2}$ ) = 1 P ( r$_{1}$ ) 〈 ∫ V d $^{3}$r ′ ∂c ∂r ′ α ∂c ∂r ′ β |∇ c ( r $^{′}$) | − 1 χ ( r$_{1}$ − r $^{′}$) 〉 ∂χ ( r$_{1}$ − r$_{2}$ ) ∂r$_{2}$$_{α}$ − ∂l ( r$_{1}$ ) ∂r$_{1}$$_{β}$ χ ( r$_{1}$ − r$_{2}$ ) − 2 3 l ( r$_{1}$ ) ∂χ ( r$_{1}$ − r$_{2}$ ) ∂r$_{2}$$_{β}$ − 2 l ( r$_{1}$ ) P ( r$_{1}$ ) p$_{αβ}$ ( r$_{1}$ ) ∂χ ( r$_{1}$ − r$_{2}$ ) ∂r$_{2}$$_{α}$ . (A8) In order to express the previous equation in terms of the coarse-grained Doi-Ohta variables { P, p , l } , we must use the following closure approximation for the first term on the right hand side 〈 ∫ V d $^{3}$r ′ ∂c ∂r ′ α ∂c ∂r ′ β |∇ c ( r $^{′}$) | − 1 χ ( r$_{1}$ − r $^{′}$) 〉 ≈ C 〈 ∫ V d $^{3}$r ′ ∂c ∂r ′ α ∂c ∂r ′ β χ ( r$_{1}$ − r $^{′}$) 〉 〈∫ V d $^{3}$r ′ |∇ c ( r $^{′}$) | χ ( r$_{1}$ − r $^{′}$) 〉 , (A9) where C is chosen in such a way that the previous expression is valid when its trace is taken. By putting α = β into the above equation, we find C = 〈∫ V d $^{3}$r ′ |∇ c ( r $^{′}$) | 2 χ ( r$_{1}$ − r $^{′}$) 〉 − 1 . (A10) Using the above expressions, element L (2) l g ( r$_{1}$ , r$_{2}$ ) takes the final form L (2) l g $_{,β}$( r$_{1}$ , r$_{2}$ ) = − l ( r$_{1}$ ) P ( r$_{1}$ ) p$_{αβ}$ ( r$_{1}$ ) ∂χ ( r$_{1}$ − r$_{2}$ ) ∂r$_{2}$$_{α}$ − 1 3 l ( r$_{1}$ ) ∂χ ( r$_{1}$ − r$_{2}$ ) ∂r$_{2}$$_{β}$ − ∂l ( r$_{1}$ ) ∂r$_{1}$$_{β}$ χ ( r$_{1}$ − r$_{2}$ ) . (A11) 26