Entropy Distance: New Quantum Phenomena
Stephan Weis and Andreas Knauf
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Submission date: 25. Oct. 2011 (revised version: September 2012)
published in: Journal of mathematical physics, 53 (2012) 10, art-no. 102206
DOI number (of the published article): 10.1063/1.4757652
MSC-Numbers: 62B10, 81P45, 94A17
Keywords and phrases: exponential family, relative entropy
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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.