  In this paper, existence of generalized solutions to a thermodynamically
consistent Navier--Stokes--Cahn--Hilliard model introduced in [18] is proven in
any space dimension. The generalized solvability concepts are measure-valued
and dissipative solutions. The measure-valued formulation incorporates an
entropy inequality and an energy inequality instead of an energy balance in a
nowadays standard way, the Gradient flow of the internal variable is fulfilled
in a weak and the momentum balance in a measure-valued sense. In the
dissipative formulation, the distributional relations of the momentum balance
and the energy as well as entropy inequality are replaced by a relative energy
inequality. Additionally, we prove the weak-strong uniqueness of the proposed
solution concepts and that all generalized solutions with additional regularity
are indeed strong solutions.
