The role of chain carriers as contributors to multiplicative closed cycles in advanced fusion fuels is examined. Emphasis is placed on rate processes which can be used to characterize critical/supercritical/subcritical tendencies of arbitrary closed fusion cycles. Temporal trajectories for the chain carriers which describe both increasing and decreasing multiplicative processes have been found to exist and identified according to their fusion fuel cycle characteristics. Practical criteria to ensure the attainment of steady-state fusion reaction processes have been formulated in terms of fusion reaction rate relationships.