| A thermodynamic approach to fast phase transitions within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables, a finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing is introduced. To describe the transition within the diffuse interface, a phase-field model which allows us to follow the steep but smooth change of phases within the width of diffuse interface is used. The governing equations of the phase-field model are derived for the hyperbolic model, model with memory, and for a model of nonlinear evolution of transition within the diffuse-interface. The consistency of the model is proved by the condition of positive entropy production and by outcomes of the fluctuation-dissipation theorem. A comparison with the existing sharp-interface and diffuse-interface versions of the model is given. |
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