  We present the derivation of the hydrodynamic limit under Eulerian scaling
for a general class of one-dimensional interacting particle systems with two or
more conservation laws. Following Yau's relative entropy method it turns out
that in case of more than one conservation laws, in order that the system
exhibit hydrodynamic behaviour, some particular identities reminiscent of
Onsager's reciprocity relations must hold. We check validity of these
identities for a wide class of models. It also follows that, as a general rule,
the equilibrium thermodynamic entropy (as function of the densities of the
conserved variables) is a globally convex Lax entropy of the hyperbolic systems
of conservation laws arising as hydrodynamic limit. The Onsager relations
arising in this context and its consequences seem to be novel. As concrete
examples we also present a number of models modeling deposition (or domain
growth) phenomena.
