论文标题
constantincarathéodory公理方法和Grigory Perelman热力学，用于几何流量和宇宙孤子解决方案
Constantin Carathéodory axiomatic approach and Grigory Perelman thermodynamics for geometric flows and cosmological solitonic solutions
论文作者
论文摘要
我们详细介绍了相对论几何流动的统计热力学模型，作为G. perelman和R. Hamilton理论的概括，围绕C.carathéodoryAxiomatic Axiomatic方法，用于具有Pfaffian微分方程的热力学。在相对论的几何流和一般相对论中，用于构建通用的非对角线和局部各向异性宇宙学的孤子解决方案，用于构建通用外部和局部各向异性宇宙学孤子解决方案的态框架变形方法AFDM。我们得出的结论是，无法用鹰 - 贝肯斯坦热力学来描述这种解决方案，用于超表面，全息，（抗）de Sitter和类似的构型。定义并计算了针对非循环RICCI流，（修改的）爱因斯坦方程以及编码孤子层次结构的局部各向异性宇宙学解决方案的新类别的几何热力学值。
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.
