
N. Iqbal et al. / Natural Science 3 (2011) 65-68
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68
Figure 2. (Color online) Comparison of equi-density entropy
changes for non-point and point mass particles (galaxies) for
an infinite gravitating system as a function of average relative
density n and the parameter b. For non-point mass
= 0.03
and R = 0.04.
R (cell size) corresponding to different values of soften-
ing parameter
. We study the variations of entropy
changes S – S0 with the changing parameter b for differ-
ent values of n and T. Some graphical variations for S –
S0 with b for different values of n = 0, 1, 100 and aver-
age temperature T = 1, 10 and 100 and by fixing value of
cell size R = 0.04 and 0.06 are shown. The graphical
analysis can be repeated for different values of R and by
fixing values of
for different sets like 0.04 and 0.05.
From both the figures shown in 1 and 2, the dashed line
represents variation for point mass particles and the solid
line represents variation for extended (non-point mass)
particles (galaxies) clustering together. It has been ob-
served that the nature of the variation remains more or
less same except with some minor difference.
4. RESULTS
The formula for entropy calculated in this paper has
provided a convenient way to study the entropy changes
in gravitational galaxy clusters in an expanding universe.
Gravity changes things that we have witnessed in this
research. Clustering of galaxies in an expanding universe,
which is like that of a self gravitating gas increases the
gases volume which increases the entropy, but it also
increases the potential energy and thus decreases the
kinetic energy as particles must work against the attrac-
tive gravitational field. So we expect expanding gases to
cool down, and therefore there is a probability that the
entropy has to decrease which gets confirmed from our
theoretical calculations as shown in Figures 1 and 2.
Entropy has remained an important contributor to our
understanding in cosmology. Everything from gravita-
tional clustering to supernova are contributors to entropy
budget of the universe. A new calculation and study of
entropy results given by Eqs.10, 12 , 16 and 17 shows
that the entropy of the universe decreases first with the
clustering rate of the particles and then gradually in-
creases as the system attains viral equilibrium. The
gravitational entropy in this paper furthermore suggests
that the universe is different than scientists had thought.
5. ACKNOWLEDGEMENTS
We are thankful to Interuniversity centre for Astronomy and Astro-
physics Pune India for providing a warm hospitality and facilities
during the course of this work.
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