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Returnability as a criterion of disequilibrium in atmospheric reactions networks

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Abstract

The concept of network returnability is reformulated as an equilibrium constant for a reaction network. Using this concept we study the atmospheric reaction networks of Earth, Mars, Venus and Titan. We found that the reaction network in the Earth’s atmosphere has the largest disequilibrium, followed by that of Titan which is still far from the most returnable atmospheres of Mars and Venus. We find that the chemical species with null or very low returnability are those in the highest disequilibrium in their respective atmospheres mainly due to physical, biogenic and/or anthropogenic mechanisms.

Graphical Abstract

Highlights: A network theoretic approach to departure from equilibrium of reaction systems. Earth's atmosphere largely departed from equilibrium. Titan's atmosphere follows Earth in disequlibrium. Venus and Mars are the most in-equilibrium atmospheres. Biogenic species departs significantly from equilibrium.

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References

  1. A.T. Balaban, in Graph Theoretical Approaches to Chemical Reactivity, ed. by D. Bonchev, O. Mekenyan (Kluwer, Dordrecht, 1994), p. 137

  2. Temkin O.N., Zeigarnik A.V., Bonchev D.G.: Chemical Reaction Networks: A Graph-Theoretical Approach. CRC Press, Boca Raton, FL (1996)

    Google Scholar 

  3. Koca J., Kratochvil M., Kvasnicka V., Matyska L., Pospichal J.: Synthon Model of Organic Chemistry and Synthesis Design. Lecture Notes in Chemistry. Springer, Berlin (1989)

    Book  Google Scholar 

  4. Estrada E.: The Structure of Complex Networks. Theory and Applications, Chapter 16. Oxford University Press, Oxford (2011)

    Google Scholar 

  5. Wayne R.P.: Chemistry of the Atmospheres. Oxford University Press, Oxford (1985)

    Google Scholar 

  6. Solé R.V., Munteanu A.: Europhys. Lett. 68, 170 (2004)

    Article  Google Scholar 

  7. Watts D.J., Strogatz S.H.: Nature 393, 440 (1998)

    Article  CAS  Google Scholar 

  8. Newman M.J.E.: Phys. Rev. Lett. 89, 208701 (2002)

    Article  CAS  Google Scholar 

  9. Gleiss P.M., Stadler P.F., Wagner A., Fell D.A.: Adv. Compl. Syst. 4, 207 (2001)

    Article  Google Scholar 

  10. Estrada E., Hatano N.: Lin. Alg. Appl. 430, 1886 (2009)

    Article  Google Scholar 

  11. Estrada E., Hatano N.: Chem. Phys. Lett. 439, 247 (2007)

    Article  CAS  Google Scholar 

  12. H. Deng, S. Radenković, I. Gutman in Applications of Graph Spectra, ed. D. Cvetković, I. Gutman (Matematički Institute SANU, Beograd, 2009), p. 123

  13. I. Gutman, H. Deng, S. Radenković in Selected Topics on Applications of Graph Spectra, ed. D. Cvetković, I. Gutman (Matematički Institute SANU, Beograd, 2011), p. 155

  14. Benzi M., Boito P.: Lin. Alg. Appl. 433, 637 (2010)

    Article  Google Scholar 

  15. Garlaschelli D., Loffredo M.I.: Phys. Rev. Lett. 93, 268701 (2004)

    Article  Google Scholar 

  16. Murphy J.G., Thornton J.A., Wooldridge P.G., Rosen R.S., Cantrell C., Shetter R.E., Lefer B., Cohen R.C.: Atmos. Chem. Phys. 4, 377 (2004)

    Article  CAS  Google Scholar 

  17. Steward R.W., Hameed S., Pinto J.: IEEE Trans. Geosc. Elec. GE-16, 30 (1978)

    Article  Google Scholar 

  18. Lovelock J.E., Margulis L.: Tellus XXVI, 1 (1974)

    Google Scholar 

  19. Russell C.T., Zhang T.L., Delva M., Magnes W., Strangeway R.J., Wei H.Y.: Nature 450, 661 (2007)

    Article  CAS  Google Scholar 

  20. Svedhem H., Titov D.V., Taylor F.W., Witassei O.: Nature 450, 629 (2007)

    Article  CAS  Google Scholar 

  21. Coustenis A., Taylor F.: The Earth-like Moon. World Sci. Pub. Co., Singapore (2000)

    Google Scholar 

  22. Clarke D., Ferris J.P.: Orig. Life Evol. Biosph. 27, 225–248 (1997)

    Article  CAS  Google Scholar 

  23. Owen T., Raulin F., McKay C.P., Lunine J.I., Bebreton J.P., Matson D.L.: ESA Bull. 24, 2905 (1997)

    Google Scholar 

  24. Lunine J.I., Nolan M.C.: Icarus 100, 221 (1992)

    Article  Google Scholar 

  25. Strobel D.F.: Planet. Space Sci. 30, 839 (1982)

    Article  CAS  Google Scholar 

  26. Lovelock J.E.: The Ages of Gaia. Norton and Co., New York (1988)

    Google Scholar 

Download references

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Correspondence to Ernesto Estrada.

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Estrada, E. Returnability as a criterion of disequilibrium in atmospheric reactions networks. J Math Chem 50, 1363–1372 (2012). https://doi.org/10.1007/s10910-012-9977-x

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  • DOI: https://doi.org/10.1007/s10910-012-9977-x

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