Duhem and Natanson: Two Mathematical Approaches to Thermodynamics

Abstract

In this article, the previously unrecognized contributions of Pierre Duhem and Ladislavus Natanson in thermodynamics are shown. The mathematical remodelling of a few of their principal ideas is taken into consideration, despite being neglected in the literature. To emphasize these ideas in an appropriate epistemological order, it would be crucial to first revalue and reconstruct some underrepresented parts of the proceedings process through which Duhem and Natanson created their thermodynamics. Duhem and Natanson’s scientific works are against the background of modern continuum mechanics, presenting relevant approaches. In line with the long-held beliefs of many French and Polish researchers, the article mentions that Duhem and Natanson’s ideas dated back to one century ago. Both scientists were qualified in the same Royal Way, which in this case includes chemistry, mechanic of fluid and solid, electro-chemistry, thermodynamics, electrodynamics, and relativistic and quantum mechanics. Therefore, it is possible to connect and then compare the results of their conceptions and approaches. Duhem and Natanson are both in firm opposition with Newtonian mechanisms. Thus, the Maupertuis least action principle created the ground for their efforts, in which they flourished as an elementary quantum.

Keywords

• thermo-chemistry thermodynamics of hidden parameters
• Duhem inequality
• Natanson’s fundamental equation
• non-linear evolution equations
• logical structure of the extended thermodynamics
• Maxwell−Natanson un-objectivity