  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 under highly non-equilibrium scenarios where
significant temperature gradients and mass transport occur across the
interface. In this work, an ab-initio thermodynamic principle is introduced
based on the entropy production at the interface that fully specifies the
associated temperature under non-equilibrium scenarios. Physically, the
thermodynamic principle provides a theoretical limit on the space of possible
phase change rates that can occur by associating the mass flux with a
corresponding interfacial entropy production rate; a stronger statement is made
that a system with sufficient degrees of freedom selects the maximum entropy
production, giving the observed phase change rate and associated interface
properties. This entropic principle captures experimental and computational
values of the interface temperature that can deviate by over $50\%$ from the
assumed saturation values. It also accounts for temperature jumps
(discontinuities) at the interface whose difference can exceed 15 degrees
Celcius. This thermodynamic principle is found to appropriately complete the
phase change problem.
