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

Abstract

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

latex2e, 11pt, 37 pages with a table of content; modified following referee's requests; accepted to EPJP. arXiv admin note: text overlap with arXiv:1907.03541

References in corpus (2)

• Ricci Flow and the Poincare Conjecture
• Curve Flows in Lagrange-Finsler Geometry, Bi-Hamiltonian Structures and Solitons

Cited by in corpus (3)

• Nonassociative black holes in R-flux deformed phase spaces and relativistic models of G. Perelman thermodynamics
• Nonassociative Ricci flows, star product and R-flux deformed black holes, and swampland conjectures
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations