  On a pre-quantized symplectic manifold, we show that the symplectic Futaki
invariant, which is an obstruction to the existence of constant Hermitian
scalar curvature almost-K\"ahler metrics, is actually an asymptotic invariant.
This allows us to deduce a lower bound for the L^2-norm of the Hermitian scalar
curvature as obtained by S. Donaldson \cite{Don} in the K\"ahler case.
