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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