Kaluza--Klein gravity & cosmology emerging from G. Perelman's entropy functionals and quantum geometric information flows

Abstract

We elaborate on quantum geometric information flows, QGIFs, and emergent (modified) Einstein-Maxwell and Kaluza-Klein, KK, theories formulated in Lagrange-Hamilton and general covariant variables. There are considered nonholonomic deformations of Grigory Perelman's F- and W-functionals (originally postulated for Riemannian metrics) for describing relativistic geometric flows, gravity and matter field interactions, and associated statistical thermodynamic systems. We argue that the concept of Perelman W-entropy presents more general and alternative possibilities to characterize geometric flow evolution, GIF, and gravity models than the Bekenstein-Hawking and another area-holographic type entropies. Formulating the theory of QGIFs, a set of fundamental geometric, probability, and quantum concepts, and methods of computation, are reconsidered for curved spacetime and (relativistic) phase spaces. Such generalized metric-affine spaces are modeled as nonholonomic Lorentz manifolds, (co) tangent Lorentz bundles, and associated vector bundles. Using geometric and entropic and thermodynamic values, we define QGIF versions of the von Neumann entropy, relative and conditional entropy, mutual information, etc. There are analyzed certain important inequalities and possible applications of G. Perelman and related entanglement and Rényi entropies to theories of KK QGIFs and emergent gravitational and electromagnetic interactions. New classes of exact cosmological solutions for GIFs and respective quasiperiodic evolution scenarios are elaborated. We show how classical and quantum thermodynamic values can be computed for cosmological quasiperiodic solutions and speculate how such constructions can be used for explaining structure formation in dark energy and dark matter physics.

arXiv commentlatex2e 11pt, v4 on 43 pages, with minor modifications requested by the referee, version accepted by EPJP

References in corpus (47)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Gaussian Quantum Information
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• On the Origin of Gravity and the Laws of Newton
• Towards a derivation of holographic entanglement entropy
• Building up spacetime with quantum entanglement
• Quantum Time Crystals
• Kaluza-Klein Gravity
• Entanglement Renormalization and Holography
• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• Emergent Gravity and the Dark Universe
• Entanglement entropy of black holes
• From Classical to Quantum Shannon Theory
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Trivializing maps, the Wilson flow and the HMC algorithm
• Classical Time Crystals
• Infinite N phase transitions in continuum Wilson loop operators
• Entanglement Equilibrium and the Einstein Equation
• 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
• A Mini-Introduction To Information Theory
• Resembling dark energy and modified gravity with Finsler-Randers cosmology
• Unification of inflation and dark energy {\it à la} quintessential inflation
• A Covariant Version of Verlinde's Emergent Gravity
• Spectral Functionals, Nonholonomic Dirac Operators, and Noncommutative Ricci Flows
• Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows
• Locally Anisotropic Kinetic Processes and Thermodynamics in Curved Spaces
• On Relativistic Generalization of Perelman's W-entropy and Statistical Thermodynamic Description of Gravitational Fields
• 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
• Inconsistencies in Verlinde's emergent gravity
• Deforming Black Hole and Cosmological Solutions by Quasiperiodic and/or Pattern Forming Structures in Modified and Einstein Gravity
• A note on a covariant version of Verlinde's emergent gravity
• On Supersymmetric Geometric Flows and ${\mathcal{R}}^2$ Inflation From Scale Invariant Supergravity
• Space-Time Quasicrystal Structures and Inflationary and Late Time Evolution Dynamics in Accelerating Cosmology
• Geometric information flows and G. Perelman entropy for relativistic classical and quantum mechanical systems
• Classical and quantum geometric information flows and entanglement of relativistic mechanical systems
• Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity
• Thermodynamics and Phase Transition in Shapere-Wilczek {\it fgh} model: Cosmological Time Crystal in Quadratic Gravity
• Anamorphic Quasiperiodic Universes in Modified and Einstein Gravity with Loop Quantum Gravity Corrections
• Starobinsky Inflation and Dark Energy and Dark Matter Effects from Quasicrystal Like Spacetime Structures
• Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows
• Phase structure of $\mathcal{N}$=1 super Yang-Mills theory from the gradient flow

Cited by in corpus (5)

• Massive quantum systems as interfaces of quantum mechanics and gravity
• The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories
• Constantin Carathéodory axiomatic approach and Grigory Perelman thermodynamics for geometric flows and cosmological solitonic solutions
• Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies
• Cosmology in $R^2$-gravity: Effects of a Higher Derivative Scalar Condensate Background