Geodesics in the Ruppeiner geometry of an ideal gas
While thermodynamic phase diagrams are efficient in representing the quasi-static transition of systems through different states, there is no immediate meaning attached to the distances between points in these state spaces. Although not unique, one may endow a meaningful metric to thermodynamic space such as the Weinhold and Ruppeiner metric. The latter, which we will use here, gives a distance that provides a lower bound on the entropy change of a system that "jumps" through different equilibrium states. If these states lie on a geodesic of this thermodynamic geometry, the lower bound of the entropy change is at a minimum. In this study, we look for the geodesics of ideal gas systems using temperature and number density as coordinates.