Conducting viscous bodies with phase transitions: Deriving Gurtin’s postulate from the second law structure invariance

We prove that the basic structures of phase-field models for phase-transitions in non-isothermal setting can be derived all together from a unique principle requiring structure invariance of the second law of thermodynamics, written as a Clausius-Duhem inequality, under orientation-preserving diffeomorphism-based changes of observer and standard regularity conditions. We thus prove that the independent scalar balance of actions driving phase transitions does not require to be postulated, as it was in Gurtin's 1996 proposal, rather it is a natural consequence of the invariance requirement adopted. The approach discussed here is also a model-building framework for the dynamics of complex bodies and allows one to show that the microstructural behavior can be responsible of effects leading to wave-type heat propagation. The results indicate another role for the second law of thermodynamics, in addition to being a source of constitutive restrictions and compatibility or stability conditions.