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In rapid phase transformations, interfaces are often driven far from equilibrium, and the chemical potential may exhibit a jump across the interface. We develop a model for the description of such situations in the framework of the phase-field formalism, with separate concentration fields in each phase. The key novel feature of this model is that the two concentration fields are linked by a kinetic equation which describes the exchange of components between the phases, instead of an equilibrium partitioning condition. The associated rate constant influences the interface dissipation. For rapid exchange between the phases, the chemical potentials are equal in both coexisting phases at the interface as in previous models, whereas in the opposite limit strong non-equilibrium behavior can be modeled. This is illustrated by simulations of a diffusion couple and of solute trapping during rapid solidification.