Entropy distance: New quantum phenomena

  • 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 infomax principles, where we contribute by computing first order optimality conditions of the entropy distance.

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Author:Stephan Weis, Andreas Knauf
Document Type:Article
Date of Publication (online):2012/11/08
Publishing Institution:Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Release Date:2012/11/08
Tag:geometry; matrix algebra; maximum entropy methods; quantum theory; set theory
Original publication:Journal of Mathematical Physics 53.10 (2012): 07.11.2012 <http://jmp.aip.org/resource/1/jmapaq/v53/i10/p102206_s1>
Institutes:Naturwissenschaftliche Fakultät -ohne weitere Spezifikation-
Dewey Decimal Classification:510 Mathematik
PACS-Classification:02.10.Ab Logic and set theory
02.40.Re Algebraic topology
03.65.Fd Algebraic methods (see also 02.20.-a Group theory)
03.65.Ta Foundations of quantum mechanics; measurement theory (for optical tests of quantum theory, see 42.50.Xa)
05.70.Ce Thermodynamic functions and equations of state (see also 51.30.+i Thermodynamic properties, equations of state in physics of gases; for equations of state of specific substances, see 64.30.-t; for equations of state of nuclear matter, and of neutron-star
Collections:Allianzlizenzen 2012

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