Log-affine geodesics in the manifold of vector states on a von Neumann algebra
arXiv:1901.06267
Abstract
This paper introduces the notion of a log-affine geodesic connecting two vector states on a von Neumann algebra. The definition is linked to the standard notion of Boltzmann-Gibbs states in statistical physics and the related notion of quantum statistical manifolds. In the abelian case it is linked to the notion of exponential tangent spaces.
13 pages