Entropy-free theories for differential materials

A thermodynamic theory was set up for general bodies of the differential type and complexity one without postulating entropy as a primitive. Indeed, a theory was proposed for such bodies in which the entropy is not postulated to exist from the outset, and in which the Clausius-Duhem inequality is replaced by a dissipative inequality involving stress, internal energy and heat flux. Entropy rate-of-change, v, is denned by means of equilibrium stress and internal energy without having at disposal a response function for the entropy, and shows that a certain condition of integrability regarding the response functions of the stress and internal energy is equivalent to the existence of a response function for the entropy. Hence, by postulating this condition to hold within the theory proposed here, we can prove the Clausius-Duhem inequality to hold, and thus also all the theorems of the corresponding classical theory. Any argument above holds in the particular case of an elastic bod