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, R\'{e}nyi 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.