Abstract
For the system of polyconvex adiabatic thermoelasticity, we defi ne a notion of dissipative measure-valued solution, which can be considered as the limit of a viscosity approximation. We embed the system into a symmetrizable hyperbolic one in order to derive the relative entropy. Exploiting the weak-stability properties of the transport and stretching identities, we base our analysis in the original variables, instead of the symmetric ones (in which the entropy is convex) and we prove measure-valued weak versus strong uniqueness using the averaged relative entropy inequality.