Appendix B We present the derivation of the expression (3.21) for the time relaxation τ$_{do}$$_{,}$$_{1}$ . Substitu- tion of the equation (3.20) for the irreversible time evolution of the configurational variable Q into the Doi-Ohta relaxation equation (1.7a) gives Under the assumption of a homogeneous system, integration over the whole system size of the above expression gives The general expression (3.19) for the coarse-grained friction matrix M (2) $^{′}$, dif gives which after substitution of the appropriate functional derivatives, M (1) , dif element, and the integration over r$_{4}$ , r ′ $_{1}$, and r ′ 2 becomes where we have used the assumption of a homogeneous ( M = const. ) and isothermal system, as well as the approximations based on a difference between the Cahn-Hilliard and Doi- Ohta length scales, as in Appendix A. Substitution of the friction matrix element (B4) into equation (B2), gives after using the normalization condition ∫ V d $^{3}$r ′ χ ( r − r ′ ) = 1, the final formula for the Doi-Ohta time relaxation 27 [1] R. G. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, New York, 1999). 1 τ$_{do}$$_{,}$$_{1}$ = 2 κ$_{E}$Ml V Q ∫ D c ρ$_{(}$$_{Q,}$$_{q}$$_{)}$ [ c ] ∫ V d $^{3}$r [ ∂ ∂ r ( ∂ $^{2}$c ( r ) ∂ r 2 )] 2 . (B5) M (2) $^{′}$, dif P ε ( r$_{1}$ , r$_{2}$ ) = ∫ D c ρ$_{(}$$_{Q,}$$_{q}$$_{)}$ [ c ] ∫ V d $^{3}$r ′ 2 κ$_{E}$MT ∂ ∂r ′ α (( ∂ $^{2}$c ∂ r $_{′}$2 ) χ ( r$_{2}$ − r $^{′}$) ) × ∂ 2 ∂r ′ $_{α}$∂r ′ β ( ∂c ∂r ′ β χ ( r$_{1}$ − r $^{′}$) ) , (B4) M (2) $^{′}$, dif P ε ( r$_{1}$ , r$_{2}$ ) = ∫ D x ρ$_{y}$ [ x ] ∫ V d $^{3}$r ′ 1 ∫ V d $^{3}$r ′ 2 χ ( r$_{1}$ − r ′ $_{1}$) χ ( r$_{2}$ − r ′ $_{2}$) × ∫ V d $^{3}$r$_{3}$ ∫ V d $^{3}$r$_{4}$ δ Π$_{P}$ [ c ]( r ′ $_{1}$) δc ( r$_{3}$ ) M (1) , dif cϵ ( r$_{3}$ , r$_{4}$ ) δ Π$_{ϵ}$[ ϵ ]( r ′ $_{2}$) δϵ ( r$_{4}$ ) , (B3) 1 τ$_{do}$$_{,}$$_{1}$ = − l QV T ∫ V d $^{3}$r$_{1}$ ∫ V d $^{3}$r$_{2}$ M (2) $^{′}$, dif P ε ( r$_{1}$ , r$_{2}$ ) . (B2) 1 τ$_{do}$$_{,}$$_{1}$ = − l ( r$_{1}$ ) Q ( r$_{1}$ ) ∫ V d $^{3}$r$_{2}$ M (2) $^{′}$, dif P ε ( r$_{1}$ , r$_{2}$ ) 1 T ( r$_{2}$ ) . (B1)