Abstract
In this talk we propose a novel method to characterize first order phasetransitions using the scalar curvature of the equilibrium thermodynamicstate space. Furthermore, our construction naturally characterizes theWidom line through the maxima of the correlation length. As anillustration, we use it in conjunction with the mean field Van der Waalsequation of state to predict the coexistence curve and the Widom line.Where closely applicable, it provides good agreement with experimentaldata. It generalizes to diverse systems like anti de Sitter black holes,which also exhibit first-order phase transitions.
