Thermodynamic curvature of the binary van der Waals fluid

TL;DR

This paper calculates the thermodynamic Ricci curvature scalar for binary van der Waals fluid mixtures in three-dimensional thermodynamic space, extending previous 2D analyses and revealing that key physical patterns persist in binary systems.

Contribution

It provides the first detailed calculation of the thermodynamic Ricci curvature scalar for binary van der Waals fluids in three dimensions, including both repulsive and attractive interactions.

Findings

Physical patterns of R in pure fluids are largely preserved in binary mixtures.

Calculations extend the application of thermodynamic geometry to more complex fluid systems.

Results suggest the robustness of thermodynamic curvature as a descriptor across different fluid types.

Abstract

The thermodynamic Ricci curvature scalar $R$ has been applied in a number of contexts, mostly for systems characterized by 2D thermodynamic geometries. Calculations of $R$ in thermodynamic geometries of dimension three or greater have been very few, especially in the fluid regime. In this paper, we calculate $R$ for two examples involving binary fluid mixtures: a binary mixture of a van der Waals (vdW) fluid with only repulsive interactions, and a binary vdW mixture with attractive interactions added. In both these examples, we evaluate $R$ for full 3D thermodynamic geometries. Our finding is that basic physical patterns found for $R$ in the pure fluid are reproduced to a large extent for the binary fluid.