  We investigate the tendency in variations of the dual CFT$_2$ when a rotating
AdS$_3$ black hole changes by fluxes transferred by the scattering of a massive
scalar field according to the AdS/CFT correspondence. The conserved quantities
of the black hole are definitely constrained by the extremal condition.
Moreover, the laws of thermodynamics provide a direction for the changes in the
conserved quantities, so the black hole cannot be extremal under the
scattering. This is naturally preferred. By the relationship between the
rotating AdS$_3$ black hole and dual CFT$_2$, we find that such changes in the
black hole constrain variations in eigenstates of the dual CFT$_2$.
Furthermore, the tendency in the variations is closely related to the laws of
thermodynamics.
