Professor Ruppeiner’s research has focused on using curved space geometry to represent physical situations in which many atoms cooperate to produce a few independent average properties, i.e., thermodynamics. Although the laws of thermodynamics make no reference to atoms, thermodynamics nevertheless yields information about microscopic properties. The curved space geometry is very revealing in this connection.
As an example, Professor Ruppeiner has applied these ideas to black holes, where the thermodynamics is well-known (due to Stephen Hawking and others), but the properties of the “atoms” is unknown. Professor Ruppeiner has also published in the areas of the large-scale arrangement of galaxies, computer approaches to "intractable" problems, theory of fluids, and using electric currents to probe the Earth.