On the indeterminateness of the constitutive equations for certain dissipative materials

Using either the classical rational thermodynamics of B. D. Coleman and W. Noll (basic argument: checking the Clausius-Duhem inequality) or the original theory of A. E. Green and P. M. Naghdi (Clausius-Duhem inequality replaced by an entropy balance law while an additional response function describes the internal rate of entropy production), the author proves several theorems such as uniqueness for the response functions of equilibrium stress, internal energy and entropy, and establishes an equality which defines the entropy in terms of internal energy and equilibrium stress. This is performed in the framework of the theory of materials such as so-called materials of the differential type and of complexity one