  Using the time evolution equations of (cosmological) General Relativity in
the first order Fischer-Marsden form, we construct an integral that measures
the amount of non-stationary energy on a given spacelike hypersurface in $D$
dimensions. The integral vanishes for stationary spacetimes; and with a further
assumption, reduces to Dain's invariant on the boundary of the hypersurface
which is defined with the Einstein constraints and a fourth order equation
defining approximate Killing symmetries.
