Information geometry in functional spaces of classical and quantum finite statistical systems

DOI10.1016/0020-7225(81)90153-1zbMath0478.46060OpenAlexW2066881202MaRDI QIDQ1161136

Roman S. Ingarden

Publication date: 1981

Published in: International Journal of Engineering Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0020-7225(81)90153-1

zbMATH Keywords

informationdensity operatorsquantum statisticsFisher information tensorfunctional geometriesjoint convexity propertypositive trace class operatorsPythagoras theorem in the largerelative entropy of statesstatistical states

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Noncommutative dynamical systems (46L55) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Applications of selfadjoint operator algebras to physics (46L60) Quantum equilibrium statistical mechanics (general) (82B10) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Information theory (general) (94A15) Statistical aspects of information-theoretic topics (62B10) Statistical thermodynamics (82B30) Axioms; other general questions in probability (60A05) Miscellaneous applications of functional analysis (46N99)

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Cites Work

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• Statistical Isomorphism
• Conditional expectation in an operator algebra. IV. Entropy and information
• Noncommutative Probability on von Neumann Algebras
• The Radon-Nikodym Theorem for Finite Rings of Operators
• Wahrscheinlichkeitstheorie
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