Information geometry and phase transitions

We present, from an information theoretic viewpoint, an analysis of phase transitions and critical phenomena in quantum systems. Our study is based on geometrical considerations within the Riemannian space of thermodynamic parameters that characterize the system. A metric for the space can be derived from an appropriate definition of distance between quantum states. For this purpose, we consider generalized alpha-divergences that include the standard Kullback-Leibler relative entropy. The use of other measures of information distance is taken into account, and the thermodynamic stability of the system is discussed from this geometric perspective.