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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Metadaten
Author:Stephan Weis, Andreas Knauf
URN:urn:nbn:de:bvb:29-opus-38482
Document Type:Article
Language:English
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
SWD-Keyword:-
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 / Naturwissenschaftliche Fakultät -ohne weitere Spezifikation-
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
PACS-Classification:00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.10.-v Logic, set theory, and algebra / 02.10.Ab Logic and set theory
00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.40.-k Geometry, differential geometry, and topology (see also section 04 Relativity and gravitation) / 02.40.Re Algebraic topology
00.00.00 GENERAL / 03.00.00 Quantum mechanics, field theories, and special relativity (see also section 11 General theory of fields and particles) / 03.65.-w Quantum mechanics [see also 03.67.-a Quantum information; 05.30.-d Quantum statistical mechanics; 31.30.J- Relativistic and quantum electrodynamics (QED) effects in atoms, molecules, and ions in atomic physics] / 03.65.Fd Algebraic methods (see also 02.20.-a Group theory)
00.00.00 GENERAL / 03.00.00 Quantum mechanics, field theories, and special relativity (see also section 11 General theory of fields and particles) / 03.65.-w Quantum mechanics [see also 03.67.-a Quantum information; 05.30.-d Quantum statistical mechanics; 31.30.J- Relativistic and quantum electrodynamics (QED) effects in atoms, molecules, and ions in atomic physics] / 03.65.Ta Foundations of quantum mechanics; measurement theory (for optical tests of quantum theory, see 42.50.Xa)
00.00.00 GENERAL / 05.00.00 Statistical physics, thermodynamics, and nonlinear dynamical systems (see also 02.50.-r Probability theory, stochastic processes, and statistics) / 05.70.-a Thermodynamics (see also section 64 Equations of state, phase equilibria, and phase transitions, and section 65 Thermal properties of condensed matter; for chemical thermodynamics, see 82.60.-s; for thermodynamics of plasmas, see 52.25.Kn; for thermodynam / 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:Universität Erlangen-Nürnberg / Allianzlizenzen / Allianzlizenzen 2012

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