Comments and Suggestions for Further Reading

Abstract

Much of the impetus for research on the mathematical foundations of thermodynamics during the past twenty years was created by the rapid development during the previous twenty years of the non-linear field theories of mechanics. That development provided a conceptual framework for the formulation of “constitutive equations,” relations which distinguish one material from another. The study of a variety of new constitutive equations together with the view that the laws of thermodynamics should place restrictions on the new equations led to the discovery of systematic procedures for finding such restrictions. In a relatively short time, these procedures were widely used, although not always without reservation. In fact, the new procedures required that one use concepts such as absolute temperature, internal energy, and entropy in contexts where traditional thermodynamics could not in any obvious way provide justification. The need to interpret these concepts for materials lying outside the scope of classical treatments, particularly for materials whose present state can depend in a non-trivial way on the entire past history of the material, was the main force behind the modern work on the foundations of thermodynamics. Many of the developments in the non-linear field theories of mechanics during the twenty years following World War II are described in great depth in the article by Truesdell and Noll [1].