  The Lie product and the order relation are viewed as defining structures for
Hamiltonian dynamical systems. Their admissible combinations are singled out by
the requirement that the group of the Lie automorphisms be contained in the
group of the order automorphisms (Lie algebras with invariant cones). Taking
advantage of the reciprocal independence of the relevant structures, the
inclusion relation between the two automorphism groups can be reversed; a
procedure which leads to an entirely new formal language (ordered linear spaces
with invariant Lie products). Presumably it offers an alternative description
for quantum systems, radically different from the conventional algebraic
models.
