Canonical form and symmetry group of systems of conservation laws

Relation between existence of an entropy and the symmetry group of a system of conservation laws is explored. For systems equipped with a single entropy, the familiar symmetric form of the system in divergence form is seen to be a useful framework for description of the symmetry group. Generalization of the symmetric form and divergence form is found appropriate for systems with multiple entropies, or for systems with a single entropy, but for which the dimension on the system exceeds that of the underlying phase space.