Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies

We investigate classical and quantum geometric information flow theories (GIFs QGIFs) when the evolution field equations for nonholonomic Einstein systems, NES, are derived from Perelman–Lyapunov-type entropic-type functionals. The term NES encodes models fundamental physical subjected to (equivalently, nonintegrable, anholonomic) constraints. There used canonical variables that allow a general decoupling integration of systems nonlinear partial differential describing GIFs QGIFs Ricci soliton-type configurations. Our approach is different constructions elaborated special classes solutions characterized by area-hypersurface entropy, related holographic, dual gauge-gravity involving generalizations Bekenstein–Hawking entropy. formulate theory which in certain quasi-classical limits with NES. computed, respectively, von Neumann, relative conditional entropy; mutual information, entanglement, Rényi construct explicit examples generic off-diagonal exact parametric stationary solitonic gravitational hierarchies deformations black hole Finally, we show how Perelman’s thermodynamic values extensions QGIF can be computed various new cannot described following approach.