The thermodynamic principle determining the interface temperatures during phase change

What is the interface temperature during phase transition (for instance, from liquid to vapor)? This question remains fundamentally unresolved. In the modeling of heat transfer problems with no phase change, the temperature and heat flux continuity conditions lead to the interface temperature. However, in problems with phase change, the heat flux condition is used to determine the amount of mass changing phase. This makes the interface temperature indeterminate unless an additional condition is imposed. A common approach in the modeling of boiling is to assume that the interface attains the saturation temperature according some measure of pressure at the interface. This assumption is usually applied even when the system is far from equilibrium, which can induce significant temperature jumps and non-monotonic temperature profiles across the interface. In this work, an ab-initio thermodynamic principle is introduced that fully specifies the associated temperatures and phase change rate under nonequilibrium scenarios. Most generally, this principle provides a theoretical limit on the space of accessible states by associating each set of discontinuous interface temperatures with a corresponding interfacial entropy production rate, calculated exactly from the entropy evolution and enthalpy jump condition across the interface. We also propose a stronger hypothesis that a system with sufficient degrees of freedom selects the maximum entropy production, giving the physically observed interface temperatures and phase change rate. This entropic principle captures experimental and computational values of the interface temperature, which can deviate by over 150 K from the assumed saturation values. It also accounts for temperature jumps (discontinuities) at the interface whose difference can exceed 15 K. This thermodynamic principle is found to appropriately complete the phase change problem.