Ruppeiner geometry

Summary

Ruppeiner geometry is the Riemannian geometry of the space of equilibrium states of a thermodynamic system. Its metric is minus the Hessian of the entropy in the extensive variables. It was introduced by George Ruppeiner and is based on the theory of thermodynamic fluctuations, in the spirit of information geometry. The distance between two nearby states measures how likely a fluctuation from one to the other is. The scalar curvature of the metric is zero for the ideal gas and is interpreted as a measure of the interactions in the system.