MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Entropy Distance: New Quantum Phenomena

Stephan Weis and Andreas Knauf


We study a curve of Gibbsian families of complex 3×3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance and non-exposed faces of the mean value set. We analyze these problems from various aspects including convex geometry, topology and information geometry. This research is motivated by a theory of info-max principles, where we contribute by computing first order optimality conditions of the entropy distance.

MSC Codes:
62B10, 81P45, 94A17
exponential family, relative entropy

Related publications

2012 Repository Open Access
Stephan Weis and Andreas Knauf

Entropy distance : new quantum phenomena

In: Journal of mathematical physics, 53 (2012) 10, p. 102206