  When a system emits gravitational radiation, the Bondi mass decreases. If the
Bondi energy is Hamiltonian, it can thus only be a time dependent Hamiltonian.
In this paper, we show that the Bondi energy can be understood as a
time-dependent Hamiltonian on the covariant phase space. Our derivation starts
from the Hamiltonian formulation in domains with boundaries that are null. We
introduce the most general boundary conditions on a generic such null boundary,
and compute quasi-local charges for boosts, energy and angular momentum.
Initially, these domains are at finite distance, such that there is a natural
IR regulator. To remove the IR regulator, we introduce a double null foliation
together with an adapted Newman--Penrose null tetrad. Both null directions are
surface orthogonal. We study the falloff conditions for such specific null
foliations and take the limit to null infinity. At null infinity, we recover
the Bondi mass and the usual covariant phase space for the two radiative modes
at the full non-perturbative level. Apart from technical results, the framework
gives two important physical insights. First of all, it explains the physical
significance of the corner term that is added in the Wald--Zoupas framework to
render the quasi-conserved charges integrable. The term to be added is simply
the derivative of the Hamiltonian with respect to the background fields that
drive the time-dependence of the Hamiltonian. Secondly, we propose a new
interpretation of the Bondi mass as the thermodynamical free energy of
gravitational edge modes at future null infinity. The Bondi mass law is then
simply the statement that the free energy always decreases on its way towards
thermal equilibrium.
