  The fundamental assumption of conventional transition state theory is the
existence of a dividing surface having the property that trajectories
originating in reactants must cross the surface only once and then proceed to
products. Recently it has been shown how to construct a dividing surface in
phase space for Hamiltonian systems with an arbitrary (but finite) number of
degrees of freedom having the property that trajectories only cross once
locally. In this letter we provide an argument showing that the flux across
this dividing surface is a minimum with respect to certain types of variations
of the dividing surface. In this sense, conventional transition state theory is
shown to be equivalent to variational transition state theory.
