Constantin Carathéodory axiomatic approach and Grigory Perelman thermodynamics for geometric flows and cosmological solitonic solutions

We elaborate on statistical thermodynamics models of relativistic geometric flows as generalizations G. Perelman and R. Hamilton theory centred around C. Carathéodory axiomatic approach to with Pfaffian differential equations. The anholonomic frame deformation method, AFDM, for constructing generic off-diagonal locally anisotropic cosmological solitonic solutions in the general relativity is developed. conclude that such cannot be described terms Hawking–Bekenstein hypersurface, holographic, (anti-) de Sitter similar configurations. thermodynamic values are defined computed nonholonomic Ricci flows, (modified) Einstein equations, new classes encoding hierarchies.