Information Geometry
The notion of Information Geometry, the study of the geometrical structure of families of probability distributions, is a long-standing one in statistics. Ruppeiner and Weinhold were the first to suggest that these ideas could also be applied in thermodynamics and statistical mechanics. The geometry of the parameter space of a statistical mechanical model in this approach gives an alternative way of characterizing phase transitions.
B. Dolan, D. Johnston and R. Kenna, The Information Geometry of the 1D Potts Model, J. Phys. A 35, 9025-9035, (2002)
W. Janke, D. Johnston and R.P.K.C. Malmini, The Information Geometry of the Ising Model on Planar Random Graphs, Phys. Rev. E66, 056119, (2002)
W. Janke, D. Johnston and R. Kenna, The Information Geometry of the Spherical Model, Phys. Rev. E67, 046106, (2003)
W. Janke, D. Johnston and R. Kenna, Information Geometry, One, Two, Three and Four, Acta Phys. Pol. 34 4923-4937, (2003)
W. Janke, D. Johnston and R. Kenna, Information Geometry and Phase Transitions, Physica A, 336 181-186, (2004)
W. Janke, D. Johnston and R. Kenna, Geometrothermodynamics of the Kehagias-Sfetsos Black Hole, J. Phys. A43 425206, (2010)