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The irreversible response of magnetic materials to magnetic fields of arbitrary time dependence is investigated by a master-equation approach. The magnetization reversal is expressed in terms of renormalized magnetization modes, and the resulting set of two-level master equations is solved by direct integration. The theory applies not only to linear energy-barrier laws but also to the physically more reasonable case where the activation energy is a nonlinear function of the applied field. Particular emphasis is on the relation between sweep-rate and magnetic-viscosity dynamics. Other regimes, such as oscillating magnetic fields, can be mapped onto sweep-rate dynamics. Magnetic-viscosity and sweep-rate experiments reflect the same fundamental magnetization processes, but energy barriers probed by dynamic experiments are smaller by about 20%.