  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.
