This paper reviews and extends the differential geometric approach to thermodynamic phase space, focusing on fluid equilibria. It examines Weinhold's energy metric, Ruppeiner's entropy metric, and the contact geometric structure, showing how Riemannian curvature encodes intermolecular interactions and critical phenomena.
Key findings
The Riemannian curvature of the equilibrium manifold encodes information about intermolecular interactions and critical phenomena.
The thermodynamic phase space possesses a natural contact structure with the Gibbs relation defining the contact form.
The scalar curvature of the thermodynamic metric diverges at critical points, indicating a geometric characterization of critical behavior.
Limitations & open questions
Further research is needed to apply these geometric concepts to non-equilibrium systems.