Thermodynamical Model of the Universe

2014

Abstract: We inquire in to the physics of a self gravitating medium in quasi-static equilibrium, using the phenomenological approach of thermodynamics. Gravitational galaxy clustering is statistical and its origin is dynamical one. Hence the aspects of clustering must be understood in order to arrive at a proper appreciation of the subject of the formation and evolution of the large scale structure of the universe. Long range gravitational forces modify the thermodynamic functions and equations of state. The thermodynamical model is discussed at many levels. First we discuss the importance of thermodynamics as applicable to the gravitational clustering problem and extend our remarks to study various thermodynamic functions like free energy, entropy, pressure, internal energy and others. The various results that we discuss have interested implications for the study of large scale structure in the universe.They support the view that an easy and simple approach can be made an alternati...

This work is devoted to the thermodynamics of gravitational clustering, a collective phenomenon with a great relevance in the N-body cosmological problem. We study a classical self-gravitating gas of identical non-relativistic particles defined on the sphere S 3 ⊂ R 4 by considering gravitational interaction that corresponds to this geometric space. The analysis is performed within microcanonical description of an isolated Hamiltonian system by combining continuum approximation and steepest descend method. According to numerical solution of resulting equations, the gravitational clustering can be associated with two microcanonical phase transitions. A first phase transition with a continuous character is associated with breakdown of SO(4) symmetry of this model. The second one is the gravitational collapse, whose continuous or discontinuous character crucially depends on the regularization of short-range divergence of gravitation potential. We also derive the thermodynamic limit of this model system, the astro-physical counterpart of Gibbs-Duhem relation, the order parameters that characterize its phase transitions and the equation of state. Other interesting behavior is the existence of states with negative heat capacities, which appear when the effects of gravitation turn dominant for energies sufficiently low. Finally, we comment the relevance of some of these results in the study of as-trophysical and cosmological situations. Special interest deserves the gravitational modification of the equation of state due to the local inhomogeneities of matter distribution. Although this feature is systematically neglected in studies about Universe expansion, the same one is able to mimic an effect that is attributed to the dark energy: a negative pressure.

General Relativity and Gravitation, 2022

The recent research on the connection between gravity and thermodynamics suggests that gravity could be an emergent phenomenon. Following this, Padmanabhan proposed a novel idea that the expansion of the universe can be interpreted as equivalent to the emergence of space with the progress of cosmic time. In this approach, the expansion of the universe is described by what is known as the law of emergence, which states that the expansion of the universe is driven by the difference between the number of bulk and surface degrees of freedom in a region bounded by the Hubble radius. This principle correctly reproduces the standard evolution of a Friedmann universe. We establish the connection of the law of emergence, which is conceptually different from the conventional paradigm to describe cosmology, with other well-established results in thermodynamics. It has been shown that the law of emergence can be derived from the unified first law of thermodynamics, which can then be considered as the backbone of the law. However, the law of emergence is rich in structure than implied by the First law thermodynamics alone. It further explains the evolution of the universe towards a state of maximum horizon entropy. Following this, it can be considered that the first law of thermodynamics, along with the additional constraints imposed by the maximisation of the horizon entropy, can together lead to the law of emergence. In the present article, we first make a brief review of Padmanabhan's proposal and then studies its connection with the thermodynamics of the horizon in the context of Einstein's, Gauss-Bonnet, and more general Lovelock gravity theories.

Natural Science, 2011

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.

General Relativity and Gravitation, 1989

A new type of cosmological history which includes large-scale entropy production is proposed. These cosmologies are based on a reinterpretation of the matter-energy stress tensor in Einstein's equations. This modifies the usual adiabatic energy conservation laws, thereby leading to a possible irreversible matter creation. This creation corresponds to an irreversible energy flow from the gravitational field to the created matter constituents. This new point of view results from the consideration of thermodynamics of open systems in the framework of cosmology. It appears that the usual initial singularity is structurally unstable with respect to irreversible matter creation. The corresponding cosmological history therefore starts from an instability of the vacuum rather than from a singularity. The universe evolves through an inflationary phase. This appears to be an attractor independent of the initial vacuum fluctuation.

We study the phase transitions occurring in the gravitational clustering of galaxies on the basis of thermodynamic fluctuation theory. This is because the fluctuations in number and energy of the particles are constantly probing the possibility of a phase transition. A calculation of various moments of the fluctuating thermodynamic extensive parameters like the number and energy fluctuations, has been performed. The correlated fluctuations �� NU � , have shown some interesting results. For weak correlations, their ensemble average is positive, indicating that a region of density enhancement typically coincides with a region of positive total energy. Its perturbed kinetic energy exceeds its perturbed potential energy. Similarly an underdense region has negative total energy since it has preferentially lost the kinetic energy of the particles that have fled. For larger correlations the overdense regions typically have negative total energy, underdense regions have positive total energ...

Physical Review D, 1996

The general principles and logical structure of a thermodynamic formalism that incorporates strongly self-gravitating systems are presented. This framework generalizes and simplifies the formulation of thermodynamics developed by Callen. The definition of extensive variables, the homogeneity properties of intensive parameters, and the fundamental problem of gravitational thermodynamics are discussed in detail. In particular, extensive parameters include quasilocal quantities and are naturally incorporated into a set of basic general postulates for thermodynamics. These include additivity of entropies (Massieu functions) and the generalized second law. Fundamental equations are no longer homogeneous first-order functions of their extensive variables. It is shown that the postulates lead to a formal resolution of the fundamental problem despite non-additivity of extensive parameters and thermodynamic potentials. Therefore, all the results of (gravitational) thermodynamics are an outgrowth of these postulates. The origin and nature of the differences with ordinary thermodynamics are analyzed. Consequences of the formalism include the (spatially) inhomogeneous character of thermodynamic equilibrium states, a reformulation of the Euler equation, and the absence of a Gibbs-Duhem relation.

Journal of Modern Physics, 2014

Within the thermodynamic model of gravity the dark energy is identified with the energy of collective gravitational interactions of all particles in the universe, which is missing in the standard treatments. For the model-universe we estimate the radiation, baryon and dark energy densities and obtain the values which are close to the current observations. It is shown that total gravitational potential of a particle from the world ensemble is a scale dependent quantity and its value is twice of Newtonian potential. The Einstein-Infeld-Hoffmann approximation to general relativity was used to show that the acceleration of a particle from the world ensemble can be considered as a relative quantity when the universe is described by the flat cosmological model.

2022

We study the effect of nonfactorizable background geometry on the thermodynamics of the clustering of galaxies. A canonical partition function is derived for the gravitating system of galaxies treated as point particles contained in cells of appropriate dimensions. Various thermodynamic equations of state, like Helmholtz free energy and entropy, among others, are also obtained. We also estimate the effect of the corrected Newton's law on the distribution function of galaxies. Remarkably, the effect of the modified Newton's law is seen only in the clustering parameter while the standard structure of the equations is preserved. A comparison of the modified clustering parameter (b *) with that of the original clustering parameter is made to visualize the effect of the correction on the time scale of clustering. The possibility of system symmetry breaking is also analyzed by investigating the behavior of the specific heat with increasing system temperature.

I discuss the statistical mechanics of gravitating systems and in particular its cosmological implications, and argue that many conventional views on this subject in the foundations of statistical mechanics embody significant confusion; I attempt to provide a clearer and more accurate account. In particular, I observe that (i) the role of gravity in entropy calculations must be distinguished from the entropy of gravity, that (ii) although gravitational collapse is entropy-increasing, this is not usually because the collapsing matter itself increases in entropy, and that (iii) the Second Law of Thermodynamics does not owe its validity to the statistical mechanics of gravitational collapse.