Entropy change and phase transitions in an expanding Universe

Abstract

The work compiles a correlated study of a gravitational quasi equilibrium thermodynamic approach for establishing and signifying a unique behavior of the cosmological entropy and phase transitions in an expanding Universe. On the basis of prescribed boundary conditions for the cluster temperature a relation for the intra-cluster medium (ICM) of galaxy clusters has been derived. A more productive and signifying approach of the correlation functions used for galaxy clustering phenomena shows a unique behavior of the entropy change where a phenomenon known as the gravitational phase transition occurs. This unique behavior occurs with a symmetry breaking from mild clustering to low clustering and from mild clustering to high clustering which differs from a normal symmetry breaking in material sciences. We also derive results for the specific latent heat associated with the phase transitions of 3.20 T c and 0.55 T c for the mildly clustered phase to the low clustered phase and from the mildly clustered phase to the highly clustered phase, respectively.

Thermodynamics and phase transitions in galaxy clustering

“…One can then see by inspection from the above equation that an infinitesimal change yields an infinitesimal change δF < 0 and that an infinitesimal change in the opposite direction yields an infinitesimal change δF > 0 as shown in Figure . This seems to be in agreement with our findings of the system's hysteresis Section 2 and in Iqbal et al (). This is consistent with Figure , showing a plot of the exact expression of vs b .…”

“…We also investigate the existence of nonanalyticities in this general parameter space and show that a cusp exists at the critical point of the mixed phase. In Section 4, we verify the previous finding of hysteresis in Iqbal et al () through an independent free energy analysis. We also highlight how our free energy analysis differs from the standard Ginzburg Landau free energy analysis.…”

“…In particular, this work adds to the literature on the study of the Cosmological Many Body Problem via the following contributions: a generalized Clausius–Clapeyron equation in a more general parameter space ( p − b parameter space) was derived. a technical study of nonanalyticities in p − b parameter space was carried out, and a very notable finding is the existence of a cusp in p − b parameter space at the critical point . The absence of any cusps except for at this point suggests the existence of a system containing a mixed phase, consistent with the conditions for the application of the Clausius–Clapeyron equation. the finding of a mixed phase and hysteresis in the system previously reported in Iqbal et al () was reproduced in this work via an independent free energy analysis. The free energy analysis in this work somewhat differs from a standard Ginzburg Landau free energy analysis, as discussed in Section 4. the results of a recent work deriving an equation for not only the slope, but the curvature of a phase coexistence curve in pressure–temperature space (see Krafcik & Velasco ()) were applied to the Cosmological Many Body Problem. an equation for the curvature of the phase coexistence curve in the context of the Cosmological Many Body Problem was derived in this work for a more general parameter space, namely p − b space. …”

“…where G is the universal gravitation constant, m is the mass of the galaxy, and is a parameter representing the halo structure of the galaxy ( = 0 corresponds to the limit of treating the galaxies as structureless point particles). Previous studies indicate that there exists a gravitational phase transition in which the nature of the clustering of the galaxies qualitatively changes as in Ahmad et al (2002), Iqbal et al (2015), Saslaw (1968Saslaw ( , 2000, Saslaw & Ahmed (2010), Saslaw & Fang (1996); Saslaw & Hamilton (1984), Saslaw & Yang (2012), and . In particular, the phase transition described was found to be a first-order phase transition.…”

“…From Iqbal et al (), the isothermal compressibility is related to b via …”