Entropy distance: New quantum phenomena
Journal Article
·
· Journal of Mathematical Physics
- Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig (Germany)
- Department of Mathematics, Friedrich-Alexander-University Erlangen-Nuremberg, Cauerstr. 11, D-91058 Erlangen (Germany)
We study a curve of Gibbsian families of complex 3 Multiplication-Sign 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 infomax principles, where we contribute by computing first order optimality conditions of the entropy distance.
- OSTI ID:
- 22093758
- Journal Information:
- Journal of Mathematical Physics, Vol. 53, Issue 10; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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