In the present work the approach-thermodynamics 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.
We study the phase transitions occurring in the gravitational clustering of galaxies on the basis of specific heat analysis and Yang–Lee theory. We find that a first‐order phase transition occurs when galaxies cluster gravitationally from an initial homogeneous phase, unlike in material sciences. At a critical temperature Tc, the system breaks the symmetry from homogeneity and there is growth of correlation functions from a linear to a non‐linear regime. These results are extended to multicomponent systems and extended mass galaxies. It is found that there is little effect of extended mass but appreciable effect of the different mass profiles of galaxies in a multicomponent system. The phase transition for a multicomponent system, dominated by more massive galaxies, occurs at an earlier stage of clustering as compared to a single‐component system. The results of Yang–Lee theory of phase transitions applied to the gravitational clustering of galaxies closely match with those from specific heat analysis.
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