On the Gibbsian thermostatics of mixtures
The work considers the problem of maximizing \(\int_{\Omega}f(y(x)) dx\), \(\Omega \subset {\mathbb{R}}^ 3\), \(y: \Omega\) \(\to {\mathbb{R}}^ m\) integrable, \(\int_{\Omega}y dx=c\), f real, continuous, in the context of thermostatics of mixtures. Necessary and sufficient conditions for the existence of maximizers are derived. The dependence of maximizers on the vector c and conditions for uniqueness are shown; these results are interpreted in the context of thermostatics and compared with such classical relations as e.g. the Clausius-Clapeyron relation.
scientific article; zbMATH DE number 3955845