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1.
Even though irreversible thermodynamics is meant to be a universal theory for nonequilibrium processes, that theory has not taken nonequilibrium radiation processes, which can normally be ignored, into account; thus it is primarily a theory for matter. When the simple bilinear entropy production rate of irreversible thermodynamics is modified, to account for the entropy production due to radiation while preserving local equilibrium for matter, the simple bilinear form of that rate, on which the current theory depends, is lost. Despite substantial compromises, generalized definitions for forces and fluxes cannot restore that simple homogeneous bilinear form, nor do they succeed in generating even generalized bilinearity in the entropy production rates for some problems concerning radiation. The possibility of a broader nonequilibrium theory is suggested by radiation problems, characterized by an example due to Planck, where those generalizations fail and the entropy production rate is a minimum in the steady state.  相似文献   

2.
De Sitter背景时空中NUT-Kerr-Newman黑洞的玻色子熵   总被引:1,自引:0,他引:1  
众所周知,一般黑洞的欧拉示性数都为2(或者为0),而NUT—Kerr—Newman黑洞是个例外,其欧拉示性数大于2.因此计算NUT—Kerr—Newman黑洞的玻色子熵有特殊的意义.运用在brick-wall方法的基础上发展起来的膜模型计算了NUT-Kerr—Newman黑洞在de Sitter时空背景下的玻色子熵.结果表明,在选取适当的截断因子的情况下,该黑洞的熵仍满足Bekenstein—Hawking面积定律.  相似文献   

3.
In recent papers we had developed a unified picture of black hole entropy and curvature which was shown to lead to Hawking radiation. It was shown that for any black hole mass, holography implies a phase space of just one quantum associated with the interior of the black hole. Here we study extremal rotating and charged black holes and obtain unique values for ratios of angular momentum to entropy, charge to entropy, etc. It turns out that these ratios can be expressed in terms of fundamental constants in nature, having analogies with other physical systems, like in condensed matter physics.  相似文献   

4.
Using the quantum statistical method, we calculate quantum statistical entropy between the black hole horizon and the cosmological horizon in Schwarzchild spacetime and derive the expression of quantum statistical entropy in de Sitter spacetime. Under the Unruh-Verlinde temperature of Schwarzchild-de Sitter spacetime in the entropic force views, we obtain the expression of quantum statistical entropy in de Sitter spacetime. It is shown that in de Sitter spacetime quantum statistical entropy is the sum of thermodynamic entropy corresponding black hole horizon and the one corresponding cosmological horizon. And the correction term of de Sitter spacetime entropy is obtained. Therefore, it is confirmed that the black hole entropy is the entropy of quantum field outside the black hole horizon. The entropy of de Sitter spacetime is the entropy of quantum field between the black hole horizon and the cosmological horizon.  相似文献   

5.
The cosmological event horizon entropy and the apparent horizon entropy of the ΛCDM and the Bianchi type I Universe model with viscosity has been calculated numerically, and analytically in the large time limit. It is shown that for these Universe models the cosmological event horizon entropy increases with time and for large times it approaches a finite maximum value. The effect of viscosity upon the entropy is also studied and we have found that its role is to decrease the entropy. The bigger the viscosity coefficient is the less the entropy will be. Furthermore, the radiation entropy for the ΛCDM Universe model with and without viscosity is investigated, and together with the cosmological event horizon entropy are used to examine the validity of the generalized second law of thermodynamics, which states that the total rate of change of entropy of the Universe is never negative, in this Universe model.  相似文献   

6.
本文利用共动度规讨论了非理想流体开放体系在自引力作用下的坍缩过程之熵变,结果表明,形成视界之前,体系的总熵不增,这说明黑洞的高熵产生于突变之中。  相似文献   

7.
The Fourier transform of cosmological density perturbations can be represented in terms of amplitudes and phases for each Fourier mode. We investigate the phase evolution of these modes using a mixture of analytical and numerical techniques. Using a toy model of one-dimensional perturbations evolving under the Zel'dovich approximation as an initial motivation, we develop a statistic that quantifies the information content of the distribution of phases. Using numerical simulations beginning with more realistic Gaussian random-phase initial conditions, we show that the information content of the phases grows from zero in the initial conditions, first slowly and then rapidly when structures become non-linear. This growth of phase information can be expressed in terms of an effective entropy. Gaussian initial conditions are a maximum entropy realization of the initial power spectrum; gravitational evolution decreases the phase entropy. We show that our definition of phase entropy results in a statistic that explicitly quantifies the information stored in the phases of density perturbations (rather than their amplitudes), and that this statistic displays interesting scaling behaviour for self-similar initial conditions.  相似文献   

8.
X-ray clusters are conventionally divided into two classes: 'cool core' (CC) clusters and 'non-cool core' (NCC) clusters. Yet relatively little attention has been given to the origins of this apparent dichotomy and, in particular, to the energetics and thermal histories of the two classes. We develop a model for the entropy profiles of clusters starting from the configuration established by gravitational shock heating and radiative cooling. At large radii, gravitational heating accounts for the observed profiles and their scalings well. However, at small and intermediate radii, radiative cooling and gravitational heating cannot be combined to explain the observed profiles of either CC or NCC clusters. The inferred entropy profiles of NCC clusters require that material is 'pre-heated' prior to cluster collapse in order to explain the absence of low-entropy (cool) material in these systems. We show that a similar modification is also required in CC clusters in order to match their entropy profiles at intermediate radii. In CC clusters, this modification is unstable, and an additional process is required to prevent cooling below a temperature of a few keV. We show that this can be achieved by adding a self-consistent active galactic nuclei (AGN) feedback loop in which the lowest entropy, most rapidly cooling material is heated and rises buoyantly to mix with material at larger radii. The resulting model does not require fine-tuning and is in excellent agreement with a wide variety of observational data from Chandra and XMM–Newton , including entropy and gas density profiles, the luminosity–temperature relation and high-resolution spectra. The spread in cluster core morphologies is seen to arise because of the steep dependence of the central cooling time on the initial level of pre-heating. Some of the other implications of this model are briefly discussed.  相似文献   

9.
It is now known that the Lyapunov characteristic numbers (LCNs) are a good indicator of stochasticity of mappings or dynamical systems. But the LCNs and the Kolmogorov entropy depend on the norm. In this paper we investigate under what coordinate transformations the LCNs and the Kolmogorov entropy are kept constant and give some numerical examples.  相似文献   

10.
Using Unruh-Verlinde temperature obtained by entropic force, we directly calculate partition functions of quantum field in Schwarzschild spacetime via quantum statistical method and derive the expression of the black hole statistical entropy. In our calculation the lower limit of integral is the location of isolated horizon introduced in loop quantum gravity and the upper limit of integral is infinity. So the obtained entropy is the statistical entropy from isolated horizon to the infinite. In our calculation there are not the cutoff and approximation. The results showed that, as long as proper Immirzi parameters are selected, the entropy obtained by loop quantum gravity is consistent with the quantum statistical entropy outside the black hole horizon. Therefore the black hole entropy is a quantum entanglement entropy outside the isolated horizon.  相似文献   

11.
Considering the fact that there is a correlation between the black hole horizon and cosmological horizon, we discuss the thermodynamic properties of de Sitter spacetime. The equivalent temperature and energy of de Sitter spacetime are obtained. It is shown that the upper limit energy of de Sitter spacetime is equal to the energy of a pure de Sitter spacetime. The thermodynamic entropy of de Sitter spacetime is the sum of the black hole horizon thermodynamic entropy and the one of cosmological horizon.  相似文献   

12.
The time-asymmetry of the universe is essentially produced by its low-entropy, unstable states. Using quantitative arguments Paul Davies has demonstrated that the expansion of the universe coupled with nuclear reaction within the stars may produce a decrease in entropy, thereby explaining its low entropy states. This idea is implemented in a qualitative way in a simple homogeneous model. Some rough coincidence with observational data is found.  相似文献   

13.
We point out that two problems of observational cosmology, namely the facts (i) that ≳60 per cent of the baryonic content of the Universe is not observed at   z ∼ 0  and (ii) that the properties of small clusters do not agree with simple expectations, could be closely related. As shown by recent studies, the shock heating associated with the formation of large-scale structures heats the intergalactic medium (IGM) and leads to a 'warm IGM' component for the gas. In the same spirit, we suggest the intracluster medium (ICM) to be a mixture of galaxy-recycled, metal-enriched gas and intergalactic gas, shock heated by the collapsing much larger scales. This could be obtained through two processes: (1) the late infalling gas from the external warm IGM is efficiently mixed within the halo and brings some additional entropy, or (2) the shocks generated by larger non-linear scales are also present within clusters and can heat the ICM. We show that, if assumption (1) holds, the entropy brought by the warm IGM is sufficient to explain the observed properties of clusters, in particular the entropy floor and the   L X– T   relation. On the other hand, we note briefly that scenario (2) would require a stronger shock heating because of the larger density of the ICM as compared with filaments. Although the efficiency of these two processes remains to be checked on a quantitative level, they have the advantage of dispensing with the need to invoke any strong preheating from supernovae or quasars (which has otherwise been introduced for the sole purpose of reproducing the behaviour of clusters). Matter ejection by galaxies is included in the present calculations and, consistently with the metal-enrichment requirements, is indeed shown to yield only a quite moderate entropy increase. Our scenario of clusters being 'born warm' can be checked through the predicted redshift evolution of the entropy floor.  相似文献   

14.
We study the relation between the existence of the logarithmic prefactor and spacetime dimensionality in black hole entropy relation by a detailed study of a TeV-scale black hole entropy. In a model universe with large extra dimensions and within the Generalized Uncertainty Principle (GUP) framework, we show that probability of black hole production in the Large Hadronic Collider (LHC) decreases for sufficiently large values of the GUP parameter. In this regard, even observation of micro-black holes may be suppressed at TeV energy scale. We determine also the GUP parameter in an extra dimensional scenario by comparing black hole entropy calculated within the GUP and loop quantum gravity frameworks.  相似文献   

15.
《New Astronomy》2007,12(1):38-46
This paper reports the study of the cold-feedback heating in cooling flow clusters. In the cold-feedback model the mass accreted by the central black hole originates in non-linear over-dense blobs of gas residing in an extended region (r  5–30 kpc); these blobs are originally hot, but then cool faster than their environment and sink toward the center. The intra-cluster medium (ICM) entropy profile must be shallow for the blobs to reach the center as cold blobs. I build a toy model to explore the role of the entropy profile and the population of dense blobs in the cold-feedback mechanism. The mass accretion rate by the central black hole is determined by the cooling time of the ICM, the entropy profile, and the presence of inhomogeneities. The mass accretion rate determines the energy injected by the black hole back to the ICM. These active galactic nucleus (AGN) outbursts not only heat the ICM, but also change the entropy profile in the cluster and cause inhomogeneities that are the seeds of future dense blobs. Therefore, in addition to the ICM temperature (or energy), the ICM entropy profile and ICM inhomogeneities are also ingredients in the feedback mechanism.  相似文献   

16.
Numerical simulations of turbulent stratified convection are used to study models with approximately the same convective flux, but different radiative fluxes. As the radiative flux is decreased, for constant convective flux: the entropy jump at the top of the convection zone becomes steeper, the temperature fluctuations increase and the velocity fluctuations decrease in magnitude, and the distance that low entropy fluid from the surface can penetrate increases. Velocity and temperature fluctuations follow mixing length scaling laws. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

17.
1 INTRODUCTIONIn theoretical physics, the thermodynamics of blajck holes remains an enigma, it turns outto be a junction of general relativity) quantum mechanics, and statistical physics.Since Bekenstein and Hawking proposed, in 1970s, that the black hole eatropy is proportional to the area of the event horizon (Bekenstein 1972, 1973, 1974; Hawking 1975; Kalloshet al. 1993), many efforts are devoted to the study of the statistical origin of the black holeentropy)One such effort is the wi…  相似文献   

18.
本文利用李立新和刘辽导出的黑洞视界附近的辐射态方程,计算了约束在一个球形盒子中的目引力辐射体系的墙(不含中心黑洞和含有中心黑洞两种情况).与Sorkin等人的计算比较,本文的结果不会出现发散困难,而且体系的总摘(包括中心黑洞的墙)的上阳正好等于坍缩后形成的同质量的黑洞嫡.作者认为,自引力辐射体系坍绩的合理模式是先形成中心黑洞,然后中心黑洞逐渐长大直至整个体系全部坍缩为黑洞.在坍缩过程中,任一中间态的媳总是比末态的黑洞墙小,到坍缩过程结束总熵才等于对应的黑洞摘.这一结果为黑洞滴的起源提供了一个合理的解释.  相似文献   

19.
Quantum entropy of extremal black holes has been discussed by many authors. However the contribution of inner event horizon has not been considered. In this paper, we consider the Reissner-Nordström-anti-de Sitter black hole, and show that the contributions lead extremal black hole entropy to obey the Nernst theorem, naturally. Therefore the contributions are important and cannot be neglected in near-extremal and extremal black hole cases.  相似文献   

20.
A Cosmological model with a viscous fluid in Kaluza-Klein metric is obtained assuming a time-dependent equation of state. The solution is in fact a generalization of an earlier work by Hajj and Boutros for a perfect fluid. It is also found that dimensional reduction of the extra space takes place such that the five-dimensional universe naturally evolves into an effective four-dimensional one. The dynamical behavior of the model is examined and it is also found that with a decrease in extra space the observable 3D space entropy increases thus accounting for the large value of entropy observable at present.  相似文献   

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