Routes towards an abstract thermodynamics in the late nineteenth century

Two different traditions of research emerged from Rudolf Clausius’s version of thermodynamics. While James Clerk Maxwell and Ludwig Boltzmann pursued the integration of thermodynamics with the kinetic theory of gases, others relied on a macroscopic and more abstract approach that set aside specific mechanical models. This second approach blossomed in about two decades in different countries of Europe and in the United States. François Massieu, Josiah Willard Gibbs, Hermann Helmholtz, and then Pierre Duhem explored the connections between the contents of thermodynamics and the formal structures of analytical mechanics. Others like the young Max Planck and Arthur von Oettingen pursued a sort of formal symmetry between thermal and mechanical variables. In the British Isles, Joseph John Thomson developed a dynamical approach to physics and chemistry, making use of the tools of abstract mechanics without excluding microscopic motions. Some developments were logically interconnected, as it was for Massieu’s, Gibbs’s, Helmholtz’s, and Duhem’s, even though they occurred in a largely independent manner. Duhem put forward the most original and most systematic reinterpretation of thermodynamics, which involved a bold upgrading of analytical mechanics and a bold mathematical unification of physics and chemistry. A strong commitment to unification was one of the hallmarks of all these theoretical researches.