Entropy of a Black Hole with Distinct Surface Gravities

In gravitational thermodynamics, the entropy of a black hole with distinct surface gravities can be evaluated in a microcanonical ensemble. At the WKB level, the entropy becomes the negative of the Euclidean action of the constrained instanton, which is the seed for the black hole creation in the no-boundary universe. Using the Gauss-Bonnet theorem, we prove the quite universal formula in Euclidean quantum gravity that the entropy of a nonrotating black hole is one quarter the sum of the products of the Euler characteristics and the areas of the horizons. For Lovelock gravity, the entropy and quantum creation of a black hole are also studied.     

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.     

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.     

Thermodynamic Gravity and the Schrödinger Equation

We adopt a formulation of the Mach principle that the rest mass of a particle is a measure of it’s long-range collective interactions with all other particles inside the horizon. As a consequence, all particles in the universe form a ‘gravitationally entangled’ statistical ensemble and one can apply the approach of classical statistical mechanics to it. It is shown that both the Schrödinger equation and the Planck constant can be derived within this Machian model of the universe. The appearance of probabilities, complex wave functions, and quantization conditions is related to the discreetness and finiteness of the Machian ensemble.     

Gibbs–Jaynes Entropy Versus Relative Entropy

The maximum entropy formalism developed by Jaynes determines the relevant ensemble in nonequilibrium statistical mechanics by maximising the entropy functional subject to the constraints imposed by the available information. We present an alternative derivation of the relevant ensemble based on the Kullback–Leibler divergence from equilibrium. If the equilibrium ensemble is already known, then calculation of the relevant ensemble is considerably simplified. The constraints must be chosen with care in order to avoid contradictions between the two alternative derivations. The relative entropy functional measures how much a distribution departs from equilibrium. Therefore, it provides a distinct approach to the calculation of statistical ensembles that might be applicable to situations in which the formalism presented by Jaynes performs poorly (such as non-ergodic dynamical systems).     

Statistical Mechanical Theory of a Closed Oscillating Universe

Based on Newton’s laws reformulated in the Hamiltonian dynamics combined with statistical mechanics, we formulate a statistical mechanical theory supporting the hypothesis of a closed universe oscillating in phase-space. We find that the behavior of this universe as a whole can be represented by a free entropic oscillator whose lifespan is nonhomogeneous, thus implying that time is shorter or longer according to the state of this universe given through its entropy. We conclude that time reduces to the entropy production of this universe and that a nonzero entropy production means that local fluctuations could exist giving rise to the appearance of masses and to the curvature of the space.     

Quantum dissipative processes and gravitational entropy of the universe

We discuss the meaning of gravitational entropy of the universe when quantum dissipative processes like cosmological particle production are important and propose to use the entropy generated in these processes as a measure of the change in gravitational entropy of the spacetime dynamics. Penrose's Weyl Curvature Hypothesis is re-examined in this generalized context. It is shown that gravitational entropy defined as such can actually decrease in the quantum regime by the action of vacuum viscosity. The theoretical and cosmological implications of this postulate is discussed.     

Entropic accelerating universe

To accommodate the observed accelerated expansion of the universe, one popular idea is to invoke a driving term in the Friedmann–Lemaître equation of dark energy which must then comprise 70% of the present cosmological energy density. We propose an alternative interpretation which takes into account the entropy and temperature intrinsic to the horizon of the universe due to the information holographically stored there. Dark energy is thereby obviated and the acceleration is due to an entropic force naturally arising from the information storage on the horizon surface screen. We consider an additional quantitative approach inspired by surface terms in general relativity and show that this leads to the entropic accelerating universe.     

A correction of (2+1) Dimensional BTZ Black Hole Entropy as a New Series with Dependence on Plank Constant

We investigate the corrected entropy and Hawking temperature of the BTZ black hole which obtained from (2 + 1) dimensional black hole. Besides, we generalize our analysis of black holes to the case of Friedmann-Robertson-Walker (FRW) universe. The corrections to the Hawking temperature and entropy of apparent horizon for FRW universe are also obtained. Comparing the results with the high energy black hole demonstrates how the semi-classic approximation affects the thermodynamics of the BTZ black hole, corrected terms, classical action and the entropy.     

Tunnelling with a negative cosmological constant

The point of this paper is to see what light new results in hyperbolic geometry may throw on gravitational entropy and whether gravitational entropy is relevant for the quantum origin of the universe. We introduce some new gravitational instantons which mediate the birth from nothing of closed universes containing wormholes and suggest that they may contribute to the density matrix of the universe. We also discuss the connection between their gravitational action and the topological and volumetric entropies introduced in hyperbolic geometry. These coincide for hyperbolic 4-manifolds, and increase with increasing topological complexity of the 4-manifold. We raise the question of whether the action also increases with the topological complexity of the initial 3-geometry, measured either by its 3-volume or its Matveev complexity. We point out, in distinction to the non-supergravity case, that universes with domains of negative cosmological constant separated by supergravity domain walls cannot be born from nothing. Finally we point out that our wormholes provide examples of the type of Perpetual Motion machines envisaged by Frolov and Novikov.     

Hawking Radiation Spectrum and Entropy Correction of Apparent Horizon in a FRW Universe

Taking the reaction of the radiation to the spacetime into consideration, we discuss Hawking radiation spectrum and Bekenstein-Hawking entropy correction in Friedmann-Robertson-Walker (FRW) universe by the analytical continuation method. We derive the radiation spectrum that satisfies the unitary principle and the logarithmic correction term of entropy in FRW universe.     

Entropy of classical systems with long-range interactions

We discuss the form of the entropy for classical Hamiltonian systems with long-range interaction using the Vlasov equation which describes the dynamics of a N particle in the limit N-->infinity. The stationary states of the Hamiltonian system are subject to infinite conserved quantities due to the Vlasov dynamics. We show that the stationary states correspond to an extremum of the Boltzmann-Gibbs entropy, and their stability is obtained from the condition that this extremum is a maximum. As a consequence, the entropy is a function of an infinite set of Lagrange multipliers that depend on the initial condition. We also discuss in this context the meaning of ensemble inequivalence and the temperature.     

Information, relative entropy of entanglement, and irreversibility

Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is shown to depend on the availability of classical information about particular members of the ensemble. Based on this, relations between relative entropy of entanglement and mutual information are derived.     

Quantum Computation Toward Quantum Gravity

The aim of this paper is to enlighten the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of Quantum Mechanics (the "It from bit" proposal). Here we suggest that quantum information must play a relevant role in Quantum Gravity (the "It from qubit" proposal). The conjecture is that Quantum Gravity, the theory which will reconcile Quantum Mechanics with General Relativity, can be formulated in terms of quantum bits of information (qubits) stored in space at the Planck scale. This conjecture is based on the following arguments: a) The holographic principle, b) The loop quantum gravity approach and spin networks, c) Quantum geometry and black hole entropy. From the above arguments, as they stand in the literature, it follows that the edges of spin networks pierce the black hole horizon and excite curvature degrees of freedom on the surface. These excitations are micro-states of Chern-Simons theory and account of the black hole entropy which turns out to be a quarter of the area of the horizon, (in units of Planck area), in accordance with the holographic principle. Moreover, the states which dominate the counting correspond to punctures of spin j = 1/2 and one can in fact visualize each micro-state as a bit of information. The obvious generalization of this result is to consider open spin networks with edges labeled by the spin –1/ 2 representation of SU(2) in a superposed state of spin "on" and spin "down." The micro-state corresponding to such a puncture will be a pixel of area which is "on" and "off" at the same time, and it will encode a qubit of information. This picture, when applied to quantum cosmology, describes an early inflationary universe which is a discrete version of the de Sitter universe.     

Holography and Non-Locality in a Closed Vacuum-Dominated Universe

A closed vacuum-dominated Friedmann universe is asymptotic to a de Sitter space with a cosmological event horizon for any observer. The holographic principle says the area of the horizon in Planck units determines the maximum number of bits of information about the universe that will ever be available to any observer. The wavefunction describing the probability distribution of mass quanta associated with bits of information on the horizon is the boundary condition for the wavefunction specifying the probability distribution of mass quanta throughout the universe. Local interactions between mass quanta in the universe cause quantum transitions in the wavefunction specifying the distribution of mass throughout the universe, with instantaneous non-local effects throughout the universe.     

Cardy–Verlinde formula in FRW Universe with inhomogeneous generalized fluid and dynamical entropy bounds near the future singularity

We derive a formula for the entropy for a multicomponent coupled fluid, which under special conditions reduces to the Cardy–Verlinde form relating the entropy of a closed FRW universe to its energy together with its Casimir energy. The generalized fluid obeys an inhomogeneous equation of state. A viscous dark fluid is included, and also modified gravity is included in terms of its fluid representation. It is demonstrated how such an expression reduces to the standard Cardy–Verlinde formula corresponding to the 2d CFT entropy in some special cases. The dynamical entropy bound for a closed FRW universe with dark components is obtained. The universality of the dynamical entropy bound near a future singularity (of all known four types), as well as near the Big Bang singularity, is investigated. It is demonstrated that, except from some special cases of Type II and Type IV singularities, the dynamical entropy bound is violated near the singularity even if quantum effects are taken into account. The dynamical entropy bound seems to be universal for the case of a regular universe, including the asymptotic de Sitter universe.     

Thermodynamics of gravitationally induced particle creation scenario in DGP braneworld

In this paper, we discuss the thermodynamical analysis for gravitationally induced particle creation scenario in the framework of DGP braneworld model. For this purpose, we consider apparent horizon as the boundary of the universe. We take three types of entropy such as Bakenstein entropy, logarithmic corrected entropy and power law corrected entropy with ordinary creation rate \(\Gamma \). We analyze the first law and generalized second law of thermodynamics analytically for these entropies which hold under some constraints. The behavior of total entropy in each case is also discussed which implies the validity of generalized second law of thermodynamics. Also, we check the thermodynamical equilibrium condition for two phases of creation rate, that is constant and variable \(\Gamma \) and found its vitality in all cases of entropy.     

Mach Like Principle from Conserved Charges

We study models where the gauge coupling constants, masses and the gravitational constant are functions of some conserved charge in the universe, and furthermore a cosmological constant that depends on the total charge of the universe. We first consider the standard Dirac action, but where the mass and the electromagnetic coupling constant are a function of the charge in the universe and afterwards extend this to curved spacetime and consider gauge coupling constants, the gravitational constant and the mass as a function of the charge of the universe, which represent a sort of Mach principle for all the constants of nature. In the flat space formulation, the formalism is not manifestly Lorentz invariant, however Lorentz invariance can be restored by performing a phase transformation of the Dirac field. One interesting model of this type is one where the action is invariant under rescalings of the Dirac wave function. In the curved space time formulation, there is the additional feature that some of the equations of motion break the general coordinate invariance also, but in a way that can be understood as a coordinate choice only, so the equations are still of the General Relativity type, but with a certain natural coordinate choice, where there is no current of the charge. We have generalized what we have done and also constructed a cosmological constant which depends on the total charge of the universe. We discuss how these ideas work when the space where the charges live is finite. If we were to use some only approximately conserved charge for these constructions, like say baryon number (in the context of the standard model), this will lead to corresponding violations of Lorentz symmetry in the early universe for example. We also briefly discuss another non-local formulations where the coupling constants are functions of the Pontryagin index of some non-abelian gauge field configurations. The construction of charge dependent contributions can also be motivated from the structure of the “infra-red counter terms” needed to cancel infra red divergences for example in three dimensions.     

Effects of quantum gravity on the inflationary parameters and thermodynamics of the early universe

The effects of generalized uncertainty principle (GUP) on the inflationary dynamics and the thermodynamics of the early universe are studied. Using the GUP approach, the tensorial and scalar density fluctuations in the inflation era are evaluated and compared with the standard case. We find a good agreement with the Wilkinson Microwave Anisotropy Probe data. Assuming that a quantum gas of scalar particles is confined within a thin layer near the apparent horizon of the Friedmann-Lemaitre-Robertson-Walker universe which satisfies the boundary condition, the number and entropy densities and the free energy arising form the quantum states are calculated using the GUP approach. A qualitative estimation for effects of the quantum gravity on all these thermodynamic quantities is introduced.