MiS Preprint Repository

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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.

Oct 25, 2011
Oct 26, 2011
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