ar X iv : c on d - m at / 9 90 20 19 v 2 2 F eb 1 99 9 Reply to Comment on ” Theory of Spinodal Decomposition ”

In his Comment [1] to my paper [2] Rutenberg notes that " the basis of my analysis of conserved scalar phase-ordering dynamics, to apply only the global conservation constraint dxψ = N, (1) is incorrect ". Because " for physical conserved systems, which evolve by mass transport, the stronger local conservation law embodied by continuity equation " ∂ψ/∂t = −∇j. (2) This question needs clarification. Replying shortly, I say that my theory has no any contradiction with the local conservation law (2). It describes the evolution of all three types of thermo-dynamic systems: without conservation law (NCOP), with global conservation law (1) (GCOP) and with local one (2) (LCOP). In these all cases the order parameter (OP) δψ(x, t) = ψ(x, t) − ψ 0 (x) dynamics near the extremal ψ 0 (x) is described by the same evolution equation ∂ψ/∂t = −ΓδF /δψ (3) with different thermodynamic potential functionals F {ψ}. For NCOP-system F {ψ} ≡ F {ψ} = dxf {ψ}, where F {ψ}is a free energy functional and f {ψ} is a specific free energy one. For GCOP-and LCOP-systems F {ψ} ≡ Ω{ψ} = F − µ g N , where the constant µ g is a global chemical potential defined by (1) and equilibrium condition δF /δψ| ψ=ψ0(x) = 0. The difference between F and Ω is that the conservation law (1) is taken into account. It should be noted that for GCOP and LCOP-systems (1) must be also used directly for selection 1