Thermodynamics Revisited

Abstract

In this chapter we shall travel the last stage of the journey which, for a physical system in equilibrium, leads us from its microscopic description to an understanding of its macroscopic properties. After having incorporated statistics in the microscopic description of the state of a system (Chap. 2), we learned how to calculate the uncertainty in that state (Chap. 3). This provided us with a criterion for assigning to a system, only known through a small number of data, the least biased probability law. For an equilibrium situation we obtained in this way the Boltzmann-Gibbs distribution (Chap. 4) which, at least in principle, enables us to evaluate the expectation value of any microscopic physical quantity. Our task, however, is not yet finished as we must still investigate the relevance of our theoretical results to our actual macroscopic experience, which is reflected in the elaborate results of thermodynamics. Let us first of all note that on a macroscopic scale the properties of the various substances do not seem to have any probabilistic character: we must thus explain how our microscopic theory, in which statistics plays such a fundamental rôle, can account for the determinism of macroscopic phenomena (§5.5).

“On a pensé que la chaleur pouvait être produite par un mouvement intestin et vibratoire des molécules des corps; mais ce système, qui paraît combattu par des observations indirectes, est maintenant généralement abandonné. Ce n’est plus qu’en Allemagne qu’il peut encore compter quelques partisans.”

C. Bailly, Manuel de Physique, 1826

“— N’avez-vous point quelques principes, quelques commencements des sciences?

— Oh! oui, je sais lire et écrire.”

Molière, Le Bourgeois Gentilhomme

“Là où je cherchais les grandes lois, on m’appellait fouilleur de détails.”

Marcel Proust, Le Temps Retrouvé