According to the theory of classic thermodynamics, any transformation is driven by the decrease of Gibbs free energy of the system. Solidification pertains to the first order transformation and obeys this basic law. The Gibbs free energy of the condensed phases of metals and alloys is closely related to the temperature and composition of the system. Thus we can describe rapid solidification process in a more precise way by using quantitative thermodynamic calculation. In combination with solidification kinetics theory, we calculated the evolution of the thermodynamic parameters during rapid solidification process. On this basis, we proposed a criterion for the end point of recalescence process and built a physical model for describing rapid solidification process and predicting recalescence temperatures of under cooled melts. Good agreement can be achieved between the present model prediction and experimental data. (C) 2016 Elsevier B.V. All rights reserved.