  I study the balance law equation of surface charges in the presence of
background fields. The construction allows a unified description of Noether's
theorem for both global and local symmetries. From the balance law associated
with some of these symmetries, I will discuss generalizations of Wald's Noether
entropy formula and general entropy balance laws on null hypersurfaces based on
the null energy conditions, interpreted as an entropy creation term. The
entropy is generally the so-called improved Noether charge, a quantity that has
recently been investigated by many authors, associated to null future-pointing
diffeomorphisms. These local and dynamical definitions of entropy on the black
hole horizon differ from the Bekenstein-Hawking entropy through terms
proportional to the first derivative of the area along the null geodesics. Two
different definitions of the dynamical entropy are identified, deduced from
gravity symplectic potentials providing a suitable notion of gravitational flux
which vanish on non-expanding horizons. The first one is proposed as a
definition of the entropy for dynamical black holes by Wald and Zhang, and it
satisfies the physical process first law locally. The second one vanishes on
any cross section of Minkowski's light cone. I study general properties of its
balance law. In particular, I look at first order perturbations around a non
expanding horizon. Furthermore, I show that the dynamical entropy increases on
the event horizon formed by a spherical symmetric collapse between the two
stationary states of vanishing flux, i.e the initial flat light cone and the
final stationary black hole. I compare this process to a phase transition, in
which the symmetry group of the stationary black hole phase is enlarged by the
supertranslations.
