Validity of the Generalized Second Law of Thermodynamics in the Logamediate and Intermediate Scenarios of the Universe

In this work, we have investigated the validity of the generalized second law of thermodynamics in logamediate and intermediate scenarios of the universe bounded by the Hubble, apparent, particle and event horizons using and without using first law of thermodynamics. We have observed that the GSL is valid for Hubble, apparent, particle and event horizons of the universe in the logamediate scenario of the universe using first law and without using first law. Similarly the GSL is valid for all horizons in the intermediate scenario of the universe using first law. Also in the intermediate scenario of the universe, the GSL is valid for Hubble, apparent and particle horizons but it breaks down whenever we consider the universe enveloped by the event horizon.     

Higher Dimensional Cosmology with Some Dark Energy Models in Emergent, Logamediate and Intermediate Scenarios of the Universe

We have considered N-dimensional Einstein field equations in which four-dimensional space-time is described by a FRW metric and that of extra dimensions by an Euclidean metric. We have chosen the exponential forms of scale factors a and d numbers of b in such a way that there is no singularity for evolution of the higher dimensional Universe. We have supposed that the Universe is filled with K-essence, Tachyonic, Normal Scalar Field and DBI-essence. Here we have found the nature of potential of different scalar field and graphically analyzed the potentials and the fields for three scenario namely Emergent Scenario, Logamediate Scenario and Intermediate Scenario. Also graphically we have depicted the geometrical parameters named statefinder parameters and slow-roll parameters in the higher dimensional cosmology with the above mentioned scenarios.     

Generalized Second Law of Thermodynamics in Emergent Universe

In this letter, we have considered the FRW model of the emergent universe, which was presented in our previous work (Debnath, in Class. Quantum Gravity 25:205019, 2008). We have chosen one of the form of scale factor in such a way that the emergent scenario is possible in the universe. We have also considered the universe as a thermodynamical system with the horizon surface as a boundary of the system. The entropy and the radius of the event horizon have been calculated in the emergent scenario. When the emergent scenario occurs, we have shown that the generalized second law of thermodynamics is always satisfied for open, flat and closed models of the universe.     

A Dark Energy Model with Generalized Uncertainty Principle in the Emergent, Intermediate and Logamediate Scenarios of the Universe

This work is motivated by the work of Kim et al. (Mod. Phys. Lett. A 23:3049, 2008), which considered the equation of state parameter for the new agegraphic dark energy based on generalized uncertainty principle coexisting with dark matter without interaction. In this work, we have considered the same dark energy interacting with dark matter in emergent, intermediate and logamediate scenarios of the universe. Also, we have investigated the statefinder, kerk and lerk parameters in all three scenarios under this interaction. The energy density and pressure for the new agegraphic dark energy based on generalized uncertainty principle have been calculated and their behaviors have been investigated. The evolution of the equation of state parameter has been analyzed in the interacting and non-interacting situations in all the three scenarios. The graphical analysis shows that the dark energy behaves like quintessence era for logamediate expansion and phantom era for emergent and intermediate expansions of the universe.     

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology

We study thermodynamics of the parabolic Lemaitre-Tolman-Bondi(LTB) cosmology supported by a perfect Suid source.This model is the natural generalization of the Sat Friedmann-Robertson-Walker(FRW) universe,and describes an inhomogeneous universe with spherical symmetry.After reviewing some basic equations in the parabolic LTB cosmology,we obtain a relation for the deceleration parameter in this model.We also obtain a condition for which the universe undergoes an accelerating phase at the present time.We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology.We find out that in LTB model of cosmology,the apparent horizon's entropy could be feeded by a term,which incorporates the effects of the inhomogeneity.We consider this result and get a relation for the total entropy evolution,which is used to examine the generalized second law of thermodynamics for an accelerating universe.We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model.     

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology

We study thermodynamics of the parabolic Lemaitre-Tolman-Bondi (LTB) cosmology supported by a perfect fluid source. This model is the natural generalization of the flat Friedmann-Robertson-Walker (FRW) universe, and describes an inhomogeneous universe with spherical symmetry. After reviewing some basic equations in the parabolic LTB cosmology, we obtain a relation for the deceleration parameter in this model. We also obtain a condition for which the universe undergoes an accelerating phase at the present time. We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology. We find out that in LTB model of cosmology, the apparent horizon's entropy could be feeded by a term, which incorporates the effects of the inhomogeneity. We consider this result and get a relation for the total entropy evolution, which is used to examine the generalized second law of thermodynamics for an accelerating universe. We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model.     

The Effects of Tachyonic and Phantom Fields in the Intermediate and Logamediate Scenarios of the Anisotropic Universe

In this work, we have analyzed two scenarios namely, “intermediate” and “logamadiate” scenarios for closed, open and flat anisotropic universe in presence of phantom field, normal tachyonic field and phantom tachyonic field. We have assumed that there is no interaction between the above mentioned dark energy and dark matter. In these two types of the scenarios of the Universe, the nature of the scalar fields and corresponding potentials have been investigated. In intermediate scenario, (i) the potential for normal tachyonic field decreases, (ii) the potentials for phantom tachyonic field and phantom field increase with the corresponding fields. Also in logamediate scenario, (i) the potential for normal tachyonic field increases, (ii) the potentials for phantom tachyonic field and phantom field decrease with the corresponding fields.     

Gauss-Bonnet and Lovelock Gravities and the Generalized Second Law of Thermodynamics

It has been shown [Chin. Phys. Lett.25 （2008） 4199] that the generalized second law of thermodynamics holds in Einstein gravity. Here we extend this procedure for Gauss-Bonnet and Lovelock gravities. It is shown that by employing the general expression for temperature Th =｜κ｜/2π= 1/2πτA （1-τA/2HτA） associated with the apparent horizon of a Friedman Robertson-Walker （FRW） universe and assuming Tm = bTh, we are able to construct conditions for which the generalized second law holds in Gauss Bonnet and Lovelock gravities, where Tm and Th are the temperatures of the source and the horizon respectively.     

Study of Tachyon Warm Intermediate and Logamediate Inflationary Universe from Loop Quantum Cosmological Perspective

We have studied the tachyon intermediate and logamediate warm inflation in loop quantum cosmological background by taking the dissipative co-efficient Γ=Γ₀ (where Γ₀ is a constant) in “intermediate” inflation and Γ=V(φ), (where V(φ) is the potential of tachyonic field) in “logamediate” inflation. We have assumed slow-roll condition to construct scalar field φ, potential V, N-folds, etc. Various slow-roll parameters have also been obtained. We have analyzed the stability of this model through graphical representations.     

Viscous Cosmology and Thermodynamics of Apparent Horizon in Modified Friedman-Robertson-Walkers Universe

In this paper, we write modified Friedman-Robertson-Walkers (FRW) equation in the form of first law of thermodynamics at the apparent horizon. We consider the universe filled with the viscous fluid. Here we employ the general expression of temperature gravity and entropy at the apparent horizon of FRW universe and obtain the generalized first law of thermodynamics at the special condition for the modified FRW equation. The generalized first law of thermodynamics help us to arrange the α ₁, α ₂, β ₁ and β ₂ in modified Friedman-Robertson-Walkers equation.     

Generalized Second Law of Thermodynamics on the Event Horizon for Interacting Dark Energy

Here we are trying to find the conditions for the validity of the generalized second law of thermodynamics (GSLT) assuming the first law of thermodynamics on the event horizon in both cases when the FRW universe is filled with interacting two fluid system- one in the form of cold dark matter and the other is either holographic dark energy or new age graphic dark energy.     

The Second Law of Thermodynamics: Foundations and Status

Over the last 10–15 years the second law of thermodynamics has undergone unprecedented scrutiny, particularly with respect to its universal status. This brief article introduces the proceedings of a recent symposium devoted to this topic, The second law of thermodynamics: Foundations and Status, held at University of San Diego as part of the 87th Annual Meeting of the Pacific Division of the AAAS (June 19–22, 2006). The papers are introduced under three themes: ideal gases, quantum perspectives, and interpretation. Roughly half the papers support traditional interpretations of the second law while the rest challenge it. Symposium proceedings from 87th Annual Meeting of the Pacific Division of the AAAS; University of San Diego, June 19–22, 2006; D.P. Sheehan, editor.     

Entropy of the Universe and Standard Cosmology

By means of a variant approach to Standard Relativistic Cosmology, we hint that the entropy of the Universe is growing with t ^3/2, where t stands for time-coordinate. Then, the absolute temperature obeys Standard t ^−1/2-dependence. We make contact with our previous paper (Berman, Int. J. Theor. Phys., 2009), in the context of a Machian Universe; but we also consider the dependencies of the scale-factor and energy density, with time, as in Standard treatments.     

Bound on the Equation of State of Dark Energy from the Generalized Second Law of Thermodynamics

Assuming that the equation of state of dark energy is a constant, we obtain the allowed interval of the equation of state of dark energy: w _D≥−1, bounded from the generalized second law of thermodynamics, in a universe enveloped by the apparent horizon and containing a Schwarzschild black hole.     

A Cosmology Governed by a Fractional Differential Equation and the Generalized Kilbas-Saigo-Mittag-Leffler Function

In this paper we discussed the FRW cosmology characterized by a scale factor obeying different independent types of fractional differential equations with solutions givens in terms of Mittag-Leffler and generalized Kilbas-Saigo-Mittag-Leffler functions. Both types of fractional operators: the Riemann-Liouville fractional integral and the Caputo fractional derivative were considered independently. Some new cosmological features were observed and discussed accordingly.     

Quantum Thermodynamics – H-Theorem and the Second Law

The second law has been demonstrated in quantum thermodynamics. The behavior of entropy is discussed.     

On the Second Law of Thermodynamics and the Piston Problem

The piston problem is investigated in the case where the length of the cylinder is infinite (on both sides) and the ratio m/M is a very small parameter, where m is the mass of one particle of the gaz and M is the mass of the piston. Introducing initial conditions such that the stochastic motion of the piston remains in the average at the origin (no drift), it is shown that the time evolution of the fluids, analytically derived from Liouville equation in a previous work, agrees with the Second Law of thermodynamics. We thus have a non equilibrium microscopical model whose evolution can be explicitly shown to obey the two laws of thermodynamics.