  We couple the issue of evolution in the laws of physics with that of
violations of energy conservation. We define evolution in terms of time
variables canonically dual to ``constants'' (such as $\Lambda$, the Planck mass
or the gravitational coupling), mimicking a procedure associated with one
formulation of unimodular gravity. We then introduce variability via a
dependence of {\it other} fundamental ``constants'' on these clocks. Although
this is not needed, sharper results are obtained if this procedure violates
local Lorentz invariance, which we define in the spirit of Horava-Lifshitz
theories (modifying a $3+1$ split action, so that a Lorentz invariant 4D
reassembly is no longer possible). We find that variability in the ``laws of
physics'' generically leads to violations of energy conservation if either a
matter parameter varies as a function of a gravitational clock, or a gravity
parameter depends on a matter clock, with the other combinations sterile. We
illustrate this with a variety of clocks (associated with matter, the speed of
light, the Ricci scalar, etc) and parameters (mainly the gravitational and
matter speed of light, but also the cosmological constant). We can accommodate
in this construction (and improve) several early Varying Speed of Light
solutions to the flatness and cosmological constant problem, allowing for
variability effects related to the spatial curvature and $\Lambda$ to cause
creation of radiation and a Hot Big Bang. But we can also go well beyond, for
example modelling signature change by a change in the sign of $c^2$, thereby
obtaining a {\it classical} realization of the Hartle-Hawking no-boundary
proposal, among other developments.
