Cosmological applications of geometrothermodynamics

H. Quevedo1, H. Quevedo2, M.N. Quevedo3

Abstract

Geometrothermodynamics is a mathematical formalism that intends to describe the properties of thermodynamic systems in terms of concepts of differential geometry. We show that it is possible to consider thermodynamic systems as extremal surfaces embedded in the thermodynamic phase space. Any extremal surface is determined by a relationship that can be interpreted as a fundamental equation from which all physical properties of the corresponding thermodynamic system can be derived. We consider particular examples from which we derive the thermodynamics of several cosmological models and show that they describe different phases of the evolution of the Universe, including inflation.

References

  1. H. Quevedo, J. Math. Phys. 48, 013506 (2007).
  2. H. B. Callen, Thermodynamics and an Introduction to Thermostatics (John Wiley & Sons, Inc., New York, 1985).
  3. C. R. Rao, Bull. Calcutta Math. Soc. 37, 81 (1945).
  4. S. Amari, Differential-Geometrical Methods in Statistics (Springer-Verlag, Berlin, 1985).
  5. F. Weinhold, J. Chem. Phys. 63, 2479, 2484, 2488, 2496 (1975); 65, 558 (1976).
  6. G. Ruppeiner, Phys. Rev. A 20, 1608 (1979).
  7. O. Luongo and H. Quevedo, Cosmological implications of geometrothermodynamics, arXiv: 1302.4866.
  8. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer Verlag, New York, 1980).
  9. R. Hermann, Geometry, physics and systems (Marcel Dekker, New York, 1973).
  10. H. Quevedo and M. N. Quevedo, Fundamentals of Geometrothermodynamics, arXiv: 1111.5056.
  11. C. V. Johnson, D-Branes (Cambridge University Press, Cambridge, UK, 2003).
  12. W. Thirring, Z. Phys. A 235, 339 (1970).
  13. D. Lynden-Bell, Physica A 263, 293 (1999).
  14. S. Capozziello, S. DeMartino, and M. Falanga, Phys. Lett. A 299, 494 (2002).
  15. S. Capozziello et al., JCAP 4, 005 (2005); astro-ph/0410503
  16. H. Quevedo and A. Ramirez, A geometric approach to the thermodynamics of the van der Waals system, arXiv: 1205.3544.
  17. A. Aviles, A. Bastarrachea, L. Campuzano, and H. Quevedo, Phys. Rev. D 86, 063508 (2012).
  18. A. Vázquez, H. Quevedo, and A. Sánchez, J. Geom. Phys. 60, 1942 (2010).
For more information about this paper please visit Springer's Home Page of this paper.



Back to The Contents Page