We proceed now to suggest plausible thermodynamic properties for continua with microstructure. Actually we should pause to consider first of all whether there could be, in thermal phenomena, an inherent complexity parallel to that of geometric and mechanical character which we have attributed throughout this tract to each element of the medium, in other words if some form of thermal microstructure exists. But that question is far too delicate and controversial; we will leave it totally open. We will rather conjecture that, even in the presence of microstructural phenomena, it be possible to measure unambiguously on each element at each instant along any process a density of internal energy ε per unit mass, a heat flux vector q, a rate of heat generation λ per unit mass due to radiation or other sources, an absolute temperature θ and a density of entropy per unit mass η. We concede that this conjecture is here far fetched (it has been criticized even within the context of ordinary continua), but we accept it nevertheless and show that it leads to some not totally unwarranted consequences.
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