Geometrothermodynamic Cosmology

Luongo O. Quevedo H.
July 2023 Multidisciplinary Digital Publishing Institute (MDPI)

Entropy
2023 #25 Issue 7

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.

fundamental equations , geometrothermodynamics , relativistic cosmology

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Scuola di Scienze e Tecnologie, Università di Camerino, Via Madonna delle Carceri 9, Camerino, 62032, Italy
SUNY Polytechnic Institute, Utica, 13502, NY, United States
INFN, Sezione di Perugia, Perugia, 06123, Italy
INAF—Osservatorio Astronomico di Brera, Milano, 20121, Italy
NNLOT, Al-Farabi Kazakh National University, Al-Farabi av. 71, Almaty, 050040, Kazakhstan
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, AP 70543, Ciudad de México, 04510, Mexico
Dipartimento di Fisica and ICRANet, Università di Roma “La Sapienza”, Roma, 00185, Italy

Scuola di Scienze e Tecnologie
SUNY Polytechnic Institute
INFN
INAF—Osservatorio Astronomico di Brera
NNLOT
Instituto de Ciencias Nucleares
Dipartimento di Fisica and ICRANet

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