On the Gibbsian thermostatics of mixtures

Abstract

In 1970, Noll [N] developed a modern version of the elements of Gibbsian thermostatics for describing the equilibrium of mixtures. An important aspect of Noll’s work is that he considered the old fundamental basis of thermostatics within a modern variational setting and, with mild hypotheses, gave proofs to some central theorems in the subject. Noll considered the stable states of a mixture to be those that maximize an entropy functional over a certain convex set of measures, and for the analysis of this variational problem he employed an elegant, albeit not standard, mathematical theory. While his work could be considered a precursor to much of the present-day studies on coexistent phases in continuum thermomechanics, nevertheless it has remained relatively, and undeservedly, obscure, perhaps because of its unusual mathematical setting.