We have a system of equations that describes the equilibration between several phases $A, B, ...$. If we define the total concentration $T = A + B + ...$, then $\partial_t T=0$ must hold.
We are further assuming equilibrium at all times, so we have devised an algorithm for this that transforms $A\rightarrow A'$, $B\rightarrow B'$ etc. Finally, the total concentration must be conserved, so we must check if $T'=T$. But should one also check if $\partial_t T'=0$, i.e. the conservation equation with the equilibrated variables?
Does it make sense to test both $T'-T=0$ and $\partial_t T'=0$?