Stability Properties of Geometrothermodynamic Cosmological Models

Article Mathematics, Applied

Geometrothermodynamic description of real gases using the law of corresponding states

Hernando Quevedo et al.

Summary: We propose a geometric model for describing the equilibrium space of real gases based on the Legendre invariant formalism of geometrothermodynamics. We investigate the curvature of three different Legendre invariant metrics and establish their relationships with critical points of response functions, isotherms in pressure-volume diagrams, and stability conditions. This implies that considering all Legendre invariant metrics is necessary for a complete description of the critical behavior and curvature singularities of real gases.

JOURNAL OF GEOMETRY AND PHYSICS (2023)

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Article Astronomy & Astrophysics

Unified representation of homogeneous and quasi-homogenous systems in geometrothermodynamics

Hernando Quevedo et al.

Summary: In this study, homogeneous and quasi-homogeneous thermodynamic systems are analyzed using the formalism of geometrothermodynamics (GTD). The explicit form of the three Legendre invariant metrics known in GTD for the equilibrium space is obtained using a generalized Euler identity. By fixing the arbitrary parameters of the GTD metrics in terms of the quasi-homogeneous coefficients, general results are obtained that relate the curvature singularities of the equilibrium space with the thermodynamic stability conditions and the phase transition structure of the system. This allows for the avoidance of non-physical singularities in the equilibrium space.

PHYSICS LETTERS B (2023)

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Review Physics, Multidisciplinary

Geometrothermodynamic Cosmology

Orlando Luongo et al.

Summary: This article reviews the main aspects of geometrothermodynamics, a formalism that employs contact geometry and Riemannian geometry to describe the properties of thermodynamic systems. It demonstrates how to handle the invariance of classical thermodynamics with respect to Legendre transformations in a geometric manner, ensuring that the properties of the systems remain unchanged regardless of the choice of thermodynamic potential. Additionally, it shows that geometrothermodynamics enables the application of a variational principle to generate thermodynamic fundamental equations, which can be used in the context of relativistic cosmology to generate cosmological models.

ENTROPY (2023)

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Article Mathematics, Applied

Geometrothermodynamics of van der Waals systems

Hernando Quevedo et al.

Summary: This paper explores the properties of the equilibrium space of van der Waals thermodynamic systems and conducts a general analysis using the law of corresponding states and the formalism of geometrothermodynamics. The investigation reveals curvature singularities in the equilibrium space corresponding to phase transitions, and the results are compared with those obtained using Hessian metrics. It is concluded that the formalism of geometrothermodynamics allows for the determination of the complete phase transition structure of systems with two thermodynamic degrees of freedom.

JOURNAL OF GEOMETRY AND PHYSICS (2022)

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Article Physics, Particles & Fields