Curvature-dimension conditions for symmetric quantum Markov semigroups

DOI10.1007/s00023-022-01220-xOpenAlexW4287180100MaRDI QIDQ2691882

Melchior Wirth, Haonan Zhang

Publication date: 30 March 2023

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.08303

Mathematics Subject Classification ID

Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57) Open systems, reduced dynamics, master equations, decoherence (81S22) Individual linear operators as elements of algebraic systems (47C99) Optimal transportation (49Q22)

Related Items

Interpolation between modified logarithmic Sobolev and Poincaré inequalities for quantum Markovian dynamics, Trace distance ergodicity for quantum Markov semigroups

Cites Work

• Unnamed Item
• Unnamed Item
• Geodesic convexity of the relative entropy in reversible Markov chains
• An analog of the 2-Wasserstein metric in non-commutative probability under which the fermionic Fokker-Planck equation is gradient flow for the entropy
• Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
• Gradient flows of the entropy for finite Markov chains
• Relating relative entropy, optimal transport and Fisher information: a quantum HWI inequality
• On the detailed balance condition for non-Hamiltonian systems
• Means of positive linear operators
• The conditional entropy power inequality for bosonic quantum systems
• Bakry-Émery curvature and diameter bounds on graphs
• Ricci curvature of finite Markov chains via convexity of the entropy
• Complete logarithmic Sobolev inequalities via Ricci curvature bounded below
• Complete gradient estimates of quantum Markov semigroups
• Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
• Noncommutative martingale deviation and Poincaré type inequalities with applications
• Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance
• Ricci curvature for metric-measure spaces via optimal transport
• An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Geometric inequalities from phase space translations
• The Entropy Power Inequality for Quantum Systems
• Transport inequalities, gradient estimates, entropy and Ricci curvature
• Subgaussian 1-cocycles on discrete groups
• Noncommutative Riesz transforms — a probabilistic approach
• A new entropy power inequality
• Entropy and index for subfactors
• A short proof of the "concavity of entropy power"
• Relative entropy for von Neumann subalgebras