  In this work, a null geometric approach to the Brown-York quasilocal
formalism is used to derive an integral law that describes the rate of change
of mass and/or radiative energy escaping through a dynamical horizon of a
non-stationary spacetime. The result thus obtained shows - in accordance with
previous results from the theory of dynamical horizons of Ashtekar et al. -
that the rate at which energy is transferred from the bulk to the boundary of
spacetime through the dynamical horizon becomes zero at equilibrium, where said
horizon becomes non-expanding and null. Moreover, it reveals previously
unrecognized quasilocal corrections to the Bondi mass-loss formula arising from
the combined variation of bulk and boundary components of the Brown-York
Hamiltonian, given in terms of a bulk-to-boundary inflow term akin to an
expression derived in an earlier paper by the author [#huber2022remark]. For
clarity, this is discussed with reference to the Generalized Vaidya family of
spacetimes, for which derived integral expressions take a particularly simple
form.
