On the geometrical structure of the generalized quantum Gibbs states (Q1112352)

Geometric methods have been used in statistical thermodynamics by \textit{R. S. Ingarden} and his collaborators [Tensor, New Ser. 30, 201-209 (1976; Zbl 0328.53054); 33, 347-352 (1979; Zbl 0436.53059); 39, 267-278 (1982; Zbl 0512.60098)]. In a recent paper the author showed that generalized classical Gibbs states may be endowed with a Riemannian structure [Rep. Math. Phys. 24, No.1, 1-10 (1986; Zbl 0637.53085)]. In this work the author studies a generalization to the quantum case. As an example he studies the geometric structure of the surface in the case of continuous quantum ideal Boson and Fermion gases and proves that the Gaussian curvature has a physical meaning.