Information measures based on Tsallis' entropy and geometric   considerations for thermodynamic systems
  An analysis of the thermodynamic behavior of quantum systems can be performed from a geometrical perspective investigating the structure of the state space. We have developed such an analysis for nonextensive thermostatistical frameworks, making use of the q-divergence derived from Tsallis' entropy. Generalized expressions for operator variance and covariance are considered, in terms of which the fundamental tensor is given. 
M. Portesi, A. Plastino, F. Pennini