Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity

Abstract

This article consists of an introduction to the theory of nonassociative geometric classical and quantum information flows defined by star products with R-flux deformations in string gravity. Corresponding nonassociative generalizations of the concepts of classical Shannon entropy, quantum von Neumann entropy, Rényi entropy are formulated. The fundamental geometric and quantum information objects are computed following the Grigori Perelman statistical thermodynamic approach to Ricci flows and gravity theories generalized for phase spaces modelled as (co) tangent Lorentz bundles. Nonassociative parametric deformations and nonholonomic thermo-geometric versions of statistical generating functions, their quantum analogues as density matrices are considered for deriving the entropy, energy and fluctuation functionals. This allows us to define and compute respective classical and quantum relative and conditional entropies, mutual information and nonassociative entanglement and thermodynamic information variables. We formulate the principles of nonassociative quantum geometric and information flow theory, QGIF, and study the basic properties of such quasi-stationary models related to modified gravity theories. Applications are considered for nonassociative deformed and entangled couples of four-dimensional, 4-d, wormholes (defined by respective spacetime and/or momentum type coordinates) and nonassociative QGIFs of 8-d phase space generalized wormholes configurations. Finally, we speculate on phase space black holes and wormholes being transversable for nonassociative qubits, quantum channels and entanglement witness; thought and laboratory experiments are discussed; and perspectives for quantum computer modelling and tests of nonassociative geometric flow and gravity theories are considered.

78 pages with table of contents, latex2e 11pt, published online in Fortsch. Phys

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Cited by in corpus (8)

• Nonassociative gauge gravity theories with R-flux star products and Batalin-Vilkovisky quantization in algebraic quantum field theory
• 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
• Nonassociative Einstein-Dirac-Maxwell systems and R-flux modified Reissner-Nordström black holes and wormholes
• Off-diagonal deformations of regular Schwarzschild black holes and general relativistic G. Perelman thermodynamics
• The fundamental physical importance of generic off-diagonal solutions and Grigori Perelman entropy in the Einstein gravity theory
• Asymptotic safe nonassociative quantum gravity with star R-flux products, Goroff-Sagnotti counter-terms, and geometric flows
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations
• Batalin-Fradkin-Vilkovisky quantization of Einstein gravity with off-diagonal solutions encoding Hořava type generating functions