[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content

Advertisement

Springer Nature Link
Log in

Does the entropy of the Universe tend to a maximum?

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

Ordinary, macroscopic systems, naturally tend to a state of maximum entropy compatible with their constraints. However, this might not hold for gravity-dominated systems since their entropy may increase without bound unless this is precluded by the formation of a black hole. In this short note we suggest, based on the Hubble expansion history, that our Universe likely behaves as an ordinary system, i.e., that its entropy seems to tend to some maximum value.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Callen, H.B.: Thermodynamics. Wiley, New York (1960)

    MATH  Google Scholar 

  2. Bekenstein, J.: Phys. Rev. D 9, 3292 (1974)

    Article  ADS  Google Scholar 

  3. Bekenstein, J.: Phys. Rev. D 12, 3077 (1975)

    Article  MathSciNet  ADS  Google Scholar 

  4. Sewell, G.L.: Phys. Lett. A 122, 309 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  5. Antonov, V.A.: Vest. Leningr. Gos. Univ. 7, 135 (1962)

    Google Scholar 

  6. Lynden-Bell, D., Wood, R.: Mon. Not. R. Astron. Soc. 138, 495 (1968)

    ADS  Google Scholar 

  7. Thorne, K.S., Zurek, W.H., Price, R.H.: The thermal atmosphere of a black hole. In: Thorne, K.S., Price, R.H., Macdonald, D.A. (eds.) Black Holes: The Membrana Paradigm. Yale University Press, New Haven (1986)

    Google Scholar 

  8. Linder, E.V.: Phys. Rev. D 82, 063514 (2010)

    Article  ADS  Google Scholar 

  9. Linder, E.V., Smith, T.L.: JCAP 04, 001 (2011)

    Article  ADS  Google Scholar 

  10. Serra, P., et al.: Phys. Rev. D 80, 121302 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  11. Riess, A.G., et al.: Astron. J. 116, 1009 (1998)

    Article  ADS  Google Scholar 

  12. Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999)

    Article  ADS  Google Scholar 

  13. Komatsu, E., et al.: Astrophys. J. Suppl. Ser. 180, 330 (2009)

    Article  ADS  Google Scholar 

  14. Amanullah, R., et al.: Astrophys. J. 716, 712 (2010)

    Article  ADS  Google Scholar 

  15. Egan, C., Lineweaver, C.L.: Astrophys. J. 710, 1825 (2010)

    Article  ADS  Google Scholar 

  16. Gibbons, G., Hawking, S.W.: Phys. Rev. D 15, 2738 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  17. Cai, R.-G.: Prog. Theor. Phys. Suppl. 172, 100 (2008)

    Article  ADS  MATH  Google Scholar 

  18. Cai, R.-G., Cao, L.-M., Hu, Y.-P.: Class. Quantum Grav. 26, 155018 (2009)

    Article  ADS  Google Scholar 

  19. Bak, D., Rey, S.-J.: Class. Quantum Grav. 17, L83 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. Simon, J., et al.: Phys. Rev. D. 71, 123001 (2005)

    Article  ADS  Google Scholar 

  21. Stern, D., et al.: JCAP 02, 008 (2010)

    Article  ADS  Google Scholar 

  22. Crawford, S.M., et al.: Mon. Not. R. Astron. Soc. 406, 2569 (2010)

    Article  ADS  Google Scholar 

  23. Carvalho, J.C., Alcaniz, J.S.: Mon. Not. R. Astron. Soc. 418, 1873 (2001)

  24. Riess, A.G., et al.: Astrophys. J. 699, 539 (2009)

    Article  ADS  Google Scholar 

  25. Wald, R.M.: General Relativity. The University of Chicago Press, Chicago (1984)

    MATH  Google Scholar 

  26. Radicella, N., Pavón, D.: Gen. Relativ. Gravit. 44, 685 (2012)

    Article  ADS  MATH  Google Scholar 

  27. Radicella, N., Pavón, D.: Phys. Lett. B 704, 206 (2011)

    Article  Google Scholar 

  28. Carroll, S.M., Hoffman, M., Trodden, M.: Phys. Rev. D 68, 023509 (2003)

    Article  ADS  Google Scholar 

  29. Cline, J.M., Jeon, S., Moore, G.D.: Phys. Rev. D 70, 043543 (2004)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

We are grateful to Fernando Atrio-Barandela and José Gaite for constructive remarks. NR is funded by the Spanish Ministry of Education through the “Subprograma Estancias de Jóvenes Doctores Extranjeros, Modalidad B”, Ref: SB2009-0056. This work was partly supported by the Spanish Ministry of Science and Innovation under Grant FIS2009-13370-C02-01, and the “Direcció de Recerca de la Generalitat” under Grant 2009SGR-00164.

Author information

Authors and Affiliations

  1. Departamento de Física, Universidad Autónoma de Barcelona, 08193 , Bellaterra, Barcelona, Spain

    Diego Pavón & Ninfa Radicella

Authors
  1. Diego Pavón
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ninfa Radicella
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ninfa Radicella.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pavón, D., Radicella, N. Does the entropy of the Universe tend to a maximum?. Gen Relativ Gravit 45, 63–68 (2013). https://doi.org/10.1007/s10714-012-1457-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10714-012-1457-x

Keywords

Search

Navigation