Entropy changes in the clustering of galaxies in an expanding universe

ABSTRACT

In the present work the approach-thermody- namics and statistical mechanics of gravitating systems is applied to study the entropy change in gravitational clustering of galaxies in an expanding universe. We derive analytically the expressions for gravitational entropy in terms of temperature T and average density n of the particles (galaxies) in the given phase space cell. It is found that during the initial stage of clustering of galaxies, the entropy decreases and finally seems to be increasing when the system attains virial equilibrium. The entropy changes are studied for different range of measuring correlation parameter b. We attempt to provide a clearer account of this phenomena. The entropy results for a system consisting of extended mass (non-point mass) particles show a similar behaviour with that of point mass particles clustering gravitationally in an expanding universe.

In the present work the approach-thermody- namics and statistical mechanics of gravitating systems is applied to study the entropy change in gravitational clustering of galaxies in an expanding universe. We derive analytically the expressions for gravitational entropy in terms of temperature T and average density n of the particles (galaxies) in the given phase space cell. It is found that during the initial stage of clustering of galaxies, the entropy decreases and finally seems to be increasing when the system attains virial equilibrium. The entropy changes are studied for different range of measuring correlation parameter b. We attempt to provide a clearer account of this phenomena. The entropy results for a system consisting of extended mass (non-point mass) particles show a similar behaviour with that of point mass particles clustering gravitationally in an expanding universe.

Cite this paper

Iqbal, N. , Khan, M. and Masood, T. (2011) Entropy changes in the clustering of galaxies in an expanding universe.*Natural Science*, **3**, 65-68. doi: 10.4236/ns.2011.31009.

Iqbal, N. , Khan, M. and Masood, T. (2011) Entropy changes in the clustering of galaxies in an expanding universe.

References

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[7] Iqbal, N., Ahmad, F. and Khan, M.S. (2006) Gravitational clustering of galaxies in an expanding universe. Journal of Astronomy and Astrophysics, 27, 373-379. doi:10.1007/BF02709363

[8] Saslaw, W.C. and Hamilton, A.J.S. (1984) Thermodynamics and galaxy clustering. Astrophysical Journal, 276, 13-25. doi:10.1086/161589

[9] Mcquarrie, D.A. and Simon, J.D. (1997) Physical chemistry: A molecular approach. University Science Books, Sausalito. Ahmad, F, Saslaw, W.C. and Bhat, N.I. (2002) Statistical mechanics of cosmological many body problem. Astrophysical Journal, 571, 576-584. doi:10.1086/340095

[10] Freud, P.G. (1970) Physics: A Contemporary Perspective. Taylor and Francis Group.

[11] Khinchin, A.I. (1949) Mathamatical Foundation of statistical mechanics. Dover Publications, New York.

[12] Frampton, P., Stephen, D.H., Kephar, T.W. and Reeb, D. (2009) Classical Quantum Gravity. 26, 145005. doi:10.1088/0264-9381/26/14/145005

[1] Voit, G.M. (2005) Tracing cosmic evolution with clusters of galaxies. Reviews of Modern Physics, 77, 207- 248.

[2] Rief, F. (1965) Fundamentals of statistical and thermal physics. McGraw-Hill, Tokyo.

[3] Spitzer, L. and Saslaw, W.C. (1966) On the evolution of galactic nuclei. Astrophysical Journal, 143, 400-420. doi:10.1086/148523

[4] Saslaw, W.C. and De Youngs, D.S. (1971) On the equipartition in galactic nuclei and gravitating systems. Astrophysical Journal, 170, 423-429. doi:10.1086/151229

[5] Itoh, M., Inagaki, S. and Saslaw, W.C. (1993) Gravitational clustering of galaxies. Astrophysical Journal, 403, 476-496. doi:10.1086/172219

[6] Hill, T.L. (1956) Statistical mechanics: Principles and statistical applications. McGraw-Hill, New York.

[7] Iqbal, N., Ahmad, F. and Khan, M.S. (2006) Gravitational clustering of galaxies in an expanding universe. Journal of Astronomy and Astrophysics, 27, 373-379. doi:10.1007/BF02709363

[8] Saslaw, W.C. and Hamilton, A.J.S. (1984) Thermodynamics and galaxy clustering. Astrophysical Journal, 276, 13-25. doi:10.1086/161589

[9] Mcquarrie, D.A. and Simon, J.D. (1997) Physical chemistry: A molecular approach. University Science Books, Sausalito. Ahmad, F, Saslaw, W.C. and Bhat, N.I. (2002) Statistical mechanics of cosmological many body problem. Astrophysical Journal, 571, 576-584. doi:10.1086/340095

[10] Freud, P.G. (1970) Physics: A Contemporary Perspective. Taylor and Francis Group.

[11] Khinchin, A.I. (1949) Mathamatical Foundation of statistical mechanics. Dover Publications, New York.

[12] Frampton, P., Stephen, D.H., Kephar, T.W. and Reeb, D. (2009) Classical Quantum Gravity. 26, 145005. doi:10.1088/0264-9381/26/14/145005