  Opposing to a (common) belief against the existence of a thermodynamic-like
potential for the KPZ equation, here we present a derivation for such a
functional. With its knowledge we prove some global shift invariance properties
previously conjectured by other authors. The procedure could be extended in
order to derive a more general form of such a functional leading to other known
related nonlinear kinetic equations. Exploiting the KPZ's functional, and for
arbitrary dimension, we have obtained the exact form of the stationary
probability distribution function and have shown a couple of examples of how it
is possible to exploit it in order to obtain relevant results like finding
support to the conjecture that in the strong coupling regime a critical
dimension doesn't exists.
