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Entropy 2014, 16(11), 5876-5890; doi:10.3390/e16115876

J.J. Thomson and Duhem’s Lagrangian Approaches to Thermodynamics

Department of Pharmacy and Biotechnology, University of Bologna—Rimini Campus, Via Dei Mille 39—47921 Rimini, Italy
This paper is an extended version of our paper published in Proceedings of the MaxEnt 2014 Conference on Bayesian Inference and Maximum Entropy Methods in Science and Engineering.
Received: 21 August 2014 / Revised: 28 October 2014 / Accepted: 4 November 2014 / Published: 6 November 2014
(This article belongs to the Special Issue Information, Entropy and Their Geometric Structures)
View Full-Text   |   Download PDF [722 KB, uploaded 24 February 2015]

Abstract

In the last decades of the nineteenth century, different attitudes towards mechanics led to two main theoretical approaches to thermodynamics: an abstract and phenomenological approach, and a very different approach in terms of microscopic models. In reality some intermediate solutions were also put forward. Helmholtz and Planck relied on a mere complementarity between mechanical and thermal variables in the expressions of state functions, and Oettingen explored the possibility of a more demanding symmetry between mechanical and thermal capacities. Planck refused microscopic interpretations of heat, whereas Helmholtz made also recourse to a Lagrangian approach involving fast hidden motions. J.J. Thomson incorporated the two mechanical attitudes in his theoretical framework, and put forward a very general theory for physical and chemical processes. He made use of two sets of Lagrangian coordinates that corresponded to two components of kinetic energy: alongside macroscopic energy, there was a microscopic energy, which was associated with the absolute temperature. Duhem put forward a bold design of unification between physics and chemistry, which was based on the two principles of thermodynamics. From the mathematical point of view, his thermodynamics or energetics consisted of a Lagrangian generalization of mechanics that could potentially describe every kind of irreversible process, explosive chemical reactions included. View Full-Text
Keywords: mechanics; thermodynamics; potentials; Lagrange’s equations; Joseph John Thomson; Pierre Duhem mechanics; thermodynamics; potentials; Lagrange’s equations; Joseph John Thomson; Pierre Duhem
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Bordoni, S. J.J. Thomson and Duhem’s Lagrangian Approaches to Thermodynamics. Entropy 2014, 16, 5876-5890.

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