Log-affine geodesics in the manifold of vector states on a von Neumann algebra

2019/01/15 by Naudts, Jan
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/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.

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