The dynamics of cyclic systems with four equivalent potential minima is studied here from two different points of view. The solution of the time-dependent Schrodinger equation provides insight into the coherent wave packet motion. The resulting reaction mechanism involves relocalization between opposite, not neighboring potential minima. The inclusion of an environment within a density matrix description leads to dissipation and therefore to a transition from coherent to incoherent dynamics. The theoretical considerations are applied to a simple model of the cyclic motion of a proton in a molecular framework.