Classical and quantum geometric information flows and entanglement of relativistic mechanical systems

Abstract

This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with methods of computation are developed in general covariant form for curved phase spaces modelled as cotangent Lorentz bundles. The constructions are based on ideas relating the Grigory Perelman's entropy for geometric flows and associated statistical thermodynamic systems to the quantum von Neumann entropy, classical and quantum relative and conditional entropy, mutual information etc. We formulate the concept of the entanglement entropy of quantum geometric information flows and study properties and inequalities for quantum, thermodynamic and geometric entropies characterising such systems.

arXiv commentlatex2e 11pt, 25 pages with a table of content, v3 closed to published journal version, with up-dated co-affiliations and references

References in corpus (33)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Three qubits can be entangled in two inequivalent ways
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Cool horizons for entangled black holes
• The Role of Relative Entropy in Quantum Information Theory
• Building up spacetime with quantum entanglement
• Ricci flow with surgery on three-manifolds
• Entanglement Renormalization and Holography
• On quantum Renyi entropies: a new generalization and some properties
• Area laws in quantum systems: mutual information and correlations
• Notes on Some Entanglement Properties of Quantum Field Theory
• Entanglement entropy of black holes
• Geometrothermodynamics
• Ricci Flow and the Poincare Conjecture
• Open-System Dynamics of Entanglement
• Entanglement entropy: holography and renormalization group
• Sandwiched Rényi Divergence Satisfies Data Processing Inequality
• Notes on Perelman's papers
• Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
• Topological Entanglement Entropy from the Holographic Partition Function
• Spectral Functionals, Nonholonomic Dirac Operators, and Noncommutative Ricci Flows
• Nonholonomic Ricci Flows: II. Evolution Equations and Dynamics
• Locally Anisotropic Kinetic Processes and Thermodynamics in Curved Spaces
• On Relativistic Generalization of Perelman's W-entropy and Statistical Thermodynamic Description of Gravitational Fields
• The Entropy of Lagrange-Finsler Spaces and Ricci Flows
• Black Holes with MDRs and Bekenstein-Hawking and Perelman Entropies for Finsler-Lagrange-Hamilton Spaces
• Geometric Flows and Perelman's Thermodynamics for Black Ellipsoids in $R^2$ and Einstein Gravity Theories
• On Supersymmetric Geometric Flows and ${\mathcal{R}}^2$ Inflation From Scale Invariant Supergravity
• Entanglement Entropy from Numerical Holography
• Quasi-Stationary Solutions in Gravity Theories with Modified Dispersion Relations and Finsler-Lagrange-Hamilton Geometry
• Schrödinger's Cat: Where Does The Entanglement Come From?

Cited by in corpus (7)

• Geometric information flows and G. Perelman entropy for relativistic classical and quantum mechanical systems
• Decoupling and integrability of nonassociative vacuum phase space gravitational equations with star and R-flux parametric deformations
• Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity
• Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies
• Nonassociative geometry of nonholonomic phase spaces with star R-flux string deformations and (non) symmetric metrics
• Constantin Carathéodory axiomatic approach and Grigory Perelman thermodynamics for geometric flows and cosmological solitonic solutions
• Kaluza--Klein gravity & cosmology emerging from G. Perelman's entropy functionals and quantum geometric information flows