  Using the Noether Charge formulation, we study a perturbation of the
conserved gravitating system. By requiring the boundary term in the variation
of the Hamiltonian to depend only on the symplectic structure, we propose a
general prescription for defining quasi-local ``conserved quantities'' (i.e. in
the situation when the gravitating system has a non-vanishing energy flux).
Applications include energy-momentum and angular momentum at spatial and null
infinity, asymptotically anti-deSitter spacetimes, and thermodynamics of the
isolated horizons.
