Hermitian Calabi functional in complexified orbits

Let $(M,\omega )$ be a compact symplectic manifold. We denote by $\text{ac}$ the space of all almost complex structure compatible with $\omega$. $\text{ac}$ has a natural foliation structure with the complexified orbit as leaf. We obtain an explicit formula of the Hessian of Hermitian Calabi functional at an extremal almost Kähler metric in $\text{ac}$. We prove that the Hessian of Hermitian Calabi functional is semi-positive definite at critical point when restricted to a complexified orbit, as corollaries we obtain some results analogy to Kähler case. We also show weak parabolicity of the Hermitian Calabi flow.