https://doi.org/10.1140/epjp/s13360-021-01527-4
Regular Article
Constantin Carathéodory axiomatic approach and Grigory Perelman thermodynamics for geometric flows and cosmological solitonic solutions
1
Radio Iaşi, 44 Lascǎr Catargi, 700107, Iaşi, Romania
2
Physics Department, California State University at Fresno, 93740, Fresno, CA, USA
3
Department of Theoretical Physics and Computer Modelling, Yu. Fedkovych Chernivtsi National University, 101 Storozhynetska street, 58029, Chernivtsi, Ukraine
4
YF CNU Ukraine, 37 Yu. Gagarina street, ap. 3, 58008, Chernivtsi, Ukraine
b sergiu.vacaru@gmail.com, sergiuvacaru@mail.fresnostate.edu
Received:
12
November
2020
Accepted:
4
May
2021
Published online:
27
May
2021
We elaborate on statistical thermodynamics models of relativistic geometric flows as generalizations 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 cannot 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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
