Fundamental properties of Tsallis relative entropy
From MaRDI portal
Publication:3024155
DOI10.1063/1.1805729zbMath1064.82001arXivcond-mat/0406178OpenAlexW2035632748MaRDI QIDQ3024155
Shigeru Furuichi, Ken Kuriyama, Kenjiro Yanagi
Publication date: 30 June 2005
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/cond-mat/0406178
Linear operator inequalities (47A63) Foundations of equilibrium statistical mechanics (82B03) Measures of information, entropy (94A17)
Related Items (69)
Fractional cumulative residual Kullback-Leibler information based on Tsallis entropy ⋮ Quantum \(f\)-divergence preserving maps on positive semidefinite operators acting on finite dimensional Hilbert spaces ⋮ The quantum ♮α-Rényi divergence of real order ⋮ On Tsallis and Kaniadakis divergences ⋮ Time evolution of relative entropies for anomalous diffusion ⋮ Relative Operator Entropy ⋮ Affinity-based extension of non-extensive entropy and statistical mechanics ⋮ Conditions for the existence of a generalization of Rényi divergence ⋮ QUANTUM DISCORD DERIVED FROM TSALLIS ENTROPY ⋮ Quantum work fluctuations versus macrorealism in terms of non-extensive entropies ⋮ Trace inequalities in nonextensive statistical mechanics ⋮ Dependence assessment based on generalized relative complexity: application to sampling network design ⋮ Lieb's concavity theorem, matrix geometric means, and semidefinite optimization ⋮ Inequalities related to some types of entropies and divergences ⋮ Maps on density operators preserving quantum \(f\)-divergences ⋮ RECORDS THEORY ⋮ Bounds of the Pinsker and Fannes types on the Tsallis relative entropy ⋮ Ordering states with Tsallis relative \(\alpha \)-entropies of coherence ⋮ The Tsallis relative 2-entropy of coherence for qubit system ⋮ On a new generalized Tsallis relative operator entropy ⋮ Geometry of \(q\)-exponential family of probability distributions ⋮ A risk profile for information fusion algorithms ⋮ On Kirkwood-Dirac quasiprobabilities and unravelings of quantum channel assigned to a tight frame ⋮ Evolution of non-stationary processes and some maximum entropy principles ⋮ Measurement-induced entropy increment for quantifying genuine coherence ⋮ On the convexity of some trace functions ⋮ Tsallis relative entropy and anomalous diffusion ⋮ A probabilistic model on streamwise velocity profile in open channels using Tsallis relative entropy theory ⋮ Refined estimations for some types of entropies and divergences ⋮ Operator entropy and fidelity associated with the geometric mean ⋮ Fano type quantum inequalities in terms of \(q\)-entropies ⋮ Variational representations related to Tsallis relative entropy ⋮ Some new Karamata type inequalities and their applications to some entropies ⋮ A generalized quantum relative entropy ⋮ On log-sum inequalities ⋮ Tsallis relative α entropy of coherence dynamics in Grover′s search algorithm ⋮ Generalization of the Kullback-Leibler divergence in the Tsallis statistics ⋮ NONADDITIVE OPEN SYSTEMS AND THE PROBLEM OF CONSTRAINTS ⋮ Choi-Davis-Jensen's inequality without convexity ⋮ Streamwise velocity profile in open-channel flow based on Tsallis relative entropy ⋮ Financial portfolios based on Tsallis relative entropy as the risk measure ⋮ Matrix trace inequalities on Tsallis relative entropy of negative order ⋮ Relative operator entropy related with the spectral geometric mean ⋮ Deformed entropy and information relations for composite and noncomposite systems ⋮ A two-parameter entropy and its fundamental properties ⋮ Inequalities for relative operator entropies and operator means ⋮ q-discord for Generalized Entropy Functions ⋮ Matrix trace inequalities related to the Tsallis relative entropies of real order ⋮ Unified \((r,s)\)-relative entropy ⋮ Reverse inequalities involving two relative operator entropies and two relative entropies ⋮ Trace inequalities for logarithms and powers of J-Hermitian matrices ⋮ New refinements of some inequalities involving relative operator entropy ⋮ Generalized Conditional Entropy — Determinicity of a Process and Rokhlin's Formula ⋮ Gradient flow formulations of discrete and continuous evolutionary models: a unifying perspective ⋮ Sufficient Conditions of the Same State Order Induced by Coherence ⋮ Inequalities for relative operator entropy in terms of Tsallis’ entropy ⋮ Entropy as an integral operator: erratum and modification ⋮ On the maximum entropy principle and the minimization of the Fisher information in Tsallis statistics ⋮ Inequalities for Tsallis relative entropy and generalized skew information ⋮ Sharp bounds for the Tsallis relative operator entropy ⋮ Generalized ‘Useful’ Relative Information Measures of Type (α, β) ⋮ A note on operator inequalities of Tsallis relative operator entropy ⋮ Coherence quantifiers from the viewpoint of their decreases in the measurement process ⋮ Two reverse inequalities associated with Tsallis relative operator entropy via generalized Kantorovich constant and their applications ⋮ An axiomatic characterization of a two-parameter extended relative entropy ⋮ Information theoretical properties of Tsallis entropies ⋮ Upper continuity bounds on the relative q-entropy for q > 1 ⋮ Tsallis entropies and matrix trace inequalities in quantum statistical mechanics ⋮ On the joint convexity of the Bregman divergence of matrices
Cites Work
- Quasi-entropies for finite quantum systems
- The proper formula for relative entropy and its asymptotics in quantum probability
- The Golden-Thompson trace inequality is complemented
- Completely positive maps and entropy inequalities
- Completely positive linear maps on complex matrices
- Matrix inequalities in statistical mechanics.
- Parametric extensions of Shannon inequality and its reverse one in Hilbert space operators.
- Generalized Shannon inequalities based on Tsallis relative operator entropy
- Possible generalization of Boltzmann-Gibbs statistics.
- Convexity inequalities for estimating free energy and relative entropy
- H-Theorem with Generalized Relative Entropies and the Tsallis Statistics
- Erratum: “Information gain within generalized thermostatistics” [J. Math. Phys. 39, 6490 (1998)]
- Inequalities for quantum entropy: A review with conditions for equality
- Conditional expectation in an operator algebra. IV. Entropy and information
- Generalized information functions
This page was built for publication: Fundamental properties of Tsallis relative entropy