Geometrothermodynamic cosmology
arXiv:2306.00839 · doi:10.3390/e25071037
Abstract
We review the main aspects of geometrothermodynamics, a formalism that uses contact geometry and Riemannian geometry to describe the properties of thermodynamic systems. We show how to handle in a geometric way the invariance of classical thermodynamics with respect to Legendre transformations, which means that the properties of the systems do not depend on the choice of the thermodynamic potential. Moreover, we show that in geometrothermodynamics it is possible to apply a variational principle to generate thermodynamic fundamental equations, which can be used in the context of relativistic cosmology to generate cosmological models. As a particular example, we consider a fundamental equation that relates the entropy with the internal energy and the volume of the Universe, and construct cosmological models with arbitrary parameters, which can be fixed to reproduce the main aspects of the inflationary era and the standard cosmological paradigm.
arXiv commentInvited review, 33 pages, 1 figure
References in corpus (30)
- Geometrothermodynamics
- Geometry of black hole thermodynamics
- Geometrothermodynamics of black holes
- Thermodynamic Curvature of the BTZ Black Hole
- Geometry of Higher-Dimensional Black Hole Thermodynamics
- On the Thermodynamic Geometry of BTZ Black Holes
- Geometrothermodynamics of asymptotically anti - de Sitter black holes
- A new approach toward geometrical concept of black hole thermodynamics
- Ruppeiner Geometry of RN Black Holes: Flat or Curved?
- Thermodynamic curvature and black holes
- Thermodynamical Metrics and Black Hole Phase Transitions
- Correspondence of phase transition points and singularities of thermodynamic geometry of black holes
- Flat Information Geometries in Black Hole Thermodynamics
- Geometric description of BTZ black holes thermodynamics
- Thermodynamic Geometry Of Charged Rotating BTZ Black Holes
- Hessian matrix, specific heats, Nambu brackets, and thermodynamic geometry
- A Commentary on Ruppeiner Metrics for Black Holes
- Geometrothermodynamics of black holes in two dimensions
- Thermodynamic systems as extremal hypersurfaces
- Extending the generalized Chaplygin gas model by using geometrothermodynamics
- Geometrothermodynamics as a singular conformal thermodynamic geometry
- Geometrothermodynamics of the Kehagias-Sfetsos Black Hole
- Quasi-Homogeneous Thermodynamics and Black Holes
- Quasi-homogeneous black hole thermodynamics
- Black Hole Thermodynamics in Carathéodory's Approach
- Homogeneity and thermodynamic identities in geometrothermodynamics
- Geometrothermodynamics of van der Waals systems
- Dark energy from Geometrothermodynamics
- Thermodynamic Geometry of the Born-Infeld-anti-de Sitter black holes
- Geometrothermodynamic model for the evolution of the Universe