  It is shown that the Kadanoff-Baym equations at consistent first-order
gradient approximation reveal exact rather than approximate conservation laws
related to global symmetries of the system. The conserved currents and
energy-momentum tensor coincide with corresponding Noether quantities in the
local approximation. These exact conservations are valid, provided a
Phi-derivable approximation is used to describe the system, and possible memory
effects in the collision term are also consistently evaluated up to first-order
gradients.
