A microscopic characterization, based on the thermodynamic curvature $R$, is proposed for first-order liquid-gas phase transitions. Near the critical point, where $R$ is proportional to the correlation volume ${\xi }^3$, we propose that $R$ takes the same value in the coexisting phases. This proposal allows a determination of the liquid-gas coexistence curve with no use of the problematic Maxwell equal area construction. Furthermore, $\left|R\right|\sim {\xi }^3$ allows a direct determination of the Widom line in the supercritical regime. We illustrate with input from the van der Waals model and the National Institute of Standards and Technology Chemistry WebBook.

• Received 11 March 2012

DOI:https://doi.org/10.1103/PhysRevE.86.052103