Basis of a non Riemannian Geometry within the Equilibrium Thermodynamics
  Microcanonical description is characterized by the presence of an internal symmetry closely related with the dynamical origin of this ensemble: the reparametrization invariance. Such symmetry possibilities the development of a non Riemannian geometric formulation within the microcanonical description of an isolated system, which leads to an unexpected generalization of the Gibbs canonical ensemble and the classical fluctuation theory for the open systems (where the inverse temperature and the total energy E behave as complementary thermodynamical quantities), the improvement of Monte Carlo simulations based on the canonical ensemble, as well as a reconsideration of any classification scheme of the phase transitions based on the concavity of the microcanonical entropy. 
L. Velazquez (Departamento de Fisica, Universidad de Pinar del Rio,   Cuba) and F. Guzman (Instituto Superior de Tecnologia ...