Conceptual polymorphism of entropy into the history: extensions of the second law of thermodynamics towards statistical physics and chemistry during nineteenth–twentieth centuries

After the birth of thermodynamics' second principle-outlined in Carnot's Reflexions sur la puissance motrice du feu (1824)-several studies provided new arguments in the field. Mainly, they concerned the thermodynamics' first principle-including energy conceptualisation-, the analytical aspects of the heat propagation, the statistical aspects of the mechanical theory of heat. In other words, the second half of nineteenth century was marked by an intense interdisciplinary research activity between physics and chemistry: new disciplines applied to the heat developed in the form of analytical, mechanical and statistical theories. Inside all these theories, entropy-the brand-new function that Clausius coined in his Mechanical theory of heat-started to play a central epistemic role. In the present paper, we analyse some steps of the historical process of conceptualisation of such function from 1850 to 1902. Particularly, we retrace the historical-foundational path that-starting from Clausius' Second Law-lead Boltzmann and Gibbs to their distinguished formulations of statistical entropy. As usual, our research has been unrolled through the analyses of primary sources and by leaning on critical readings of the secondary literature. As for the methodological approach, text analysis of historical documents constituted our privileged modus operandi. This paper is the expression of a collaborative historical research program focused on the thermodynamic foundations of physics-chemistry relationship; early results have already been published by the same authors upon the concepts of reversibility--and--thermal equilibrium.