Discussion of Garfinkle-Horowitz-Strominger Dilaton Black Hole Entropy

We discuss the entropy of the Garfinkle-Horowitz-Strominger dilaton black hole by using the thin film brick-wall model, and the entropy obtained is proportional to the horizon area of the black hole confirming the Bekenstein-Hawking＇s area-entropy formula. Then, by comparing with the original brick-wall method, we find that the result obtained by the thin film method is more reasonable avoiding some drawbacks, such as little mass approximation, neglecting logarithm term, and taking the term L^3 as a contribution of the vacuum surrounding the black hole, and the physical meaning of the entropy is more clearer.     

The Free Energy and Entropy of Schwarzschild Black Hole Due to Scalar Field

Using the thin film brick-wall model,taking into account the effect of the generalized uncertainty principle on the equation of the density of the states, we calculate the free energy and entropy of schwarzschild black hole due to scalar field, we obtain the entropy proportional to the event horizon area without cutoff. This implies that quantum theory of gravity can remove the divergence of the state density on the event horizon and avoid the cutoff in the original brick-wall model, these results also mean that the thin film brick-wall model is universal. PACS: 0420;9760L.     

Entropy of Dirac Field in Non-stationary and Slowly Changing Reissner-Nordstrom Black Hole

Using the thin film brick-wall model and WKB approximation, the entropy of the Dirac field in the nonstationary and slowly changing Reissner-Nordstrom （R-N） black hole is calculated. The result shows that the entropy of the R-N black hole is still proportional to its surface area if we choose proper cut-off.     

Entropy of Dirac Field in Non-stationary and Slowly Changing Reissner-Nordstrom Black Hole

Using the thin film brick-wall model and WKB approximation, the entropy of the Dirac field in the non-stationary and slowly changing Reissner-Nordstrom (R-N) black hole is calculated. The result shows that the entropy of the R-N black hole is still proportional to its surface area if we choose proper cut-off.     

Entropy of charged dilaton-axion black hole with minimal length revisited

Using the generalized uncertainty principle, we calculate the entropy of the charged dilaton-axion black hole for both asymptotically flat and non-flat cases by counting degrees of freedom near the horizon. The divergence of density of states and free energy appearing in the thin film brick-wall model is removed without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.      

相空间中脑电近似熵和信息熵的计算

提出一种基于相空间重构脑电信号来计算脑电近似熵和信息熵的新方法．实验计算结果表明,癫痫患者脑电和正常人脑电的近似熵和信息熵随相空间嵌入维数的变化有明显的不同．     

Regularization of Quantum Relative Entropy in Finite Dimensions and Application to Entropy Production

The fundamental concept of relative entropy is extended to a functional that is regular-valued also on arbitrary pairs of nonfaithful states of open quantum systems. This regularized version preserves almost all important properties of ordinary relative entropy such as joint convexity and contractivity under completely positive quantum dynamical semigroup time evolution. On this basis a generalized formula for entropy production is proposed, the applicability of which is tested in models of irreversible processes. The dynamics of the latter is determined by either Markovian or non-Markovian master equations and involves all types of states.     

Positivity of Entropy Production

We discuss the positivity of the mean entropy production for stochastic systems driven from equilibrium, as it was defined in refs. 7 and 8. Non-zero entropy production is closely linked with violation of the detailed balance condition. This connection is rigorously obtained for spinflip dynamics. We remark that the positivity of entropy production depends on the choice of time-reversal transformation, hence on the choice of the dynamical variables in the system of interest.     

Expanding the Area of Gravitational Entropy

I describe how gravitational entropy is intimately connected with the concept of gravitational heat, expressed as the difference between the total and free energies of a given gravitational system. From this perspective one can compute these thermodyanmic quantities in settings that go considerably beyond Bekenstein's original insight that the area of a black hole event horizon can be identified with thermodynamic entropy. The settings include the outsides of cosmological horizons and spacetimes with NUT charge. However the interpretation of gravitational entropy in these broader contexts remains to be understood.     

On Thermodynamic Limits of Entropy Densities

We give some sufficient conditions which guarantee that the entropy density in the thermodynamic limit is equal to the thermodynamic limit of the entropy densities of finite-volume (local) Gibbs states.     

Differential Entropy and Dynamics of Uncertainty

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L ²(R ⁿ ) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases. PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a     

On the Origin of Black-Hole Entropy

A simple statistical interpretation of the origin of black hole entropy is presented. It is shown that this entropy can be understood as emerging as a result of missing information about the exact state of the matter from which the black hole was formed.     

Comments on the Statistical Origin of Black Hole Entropy

This paper shows that the black hole entropy can be interpreted as emerging as a result of missing information about the exact state of the matter from which the black hole was formed.     

The Topological Version of Free Entropy

Notions of topological free entropy and of free capacity are introduced in the C*-algebra context. Basic properties, basic problems and connections to potential theory and random matrix theory are discussed.     

The Concavity of Entropy and Extremum Principles in Thermodynamics

We revisit the concavity property of the thermodynamic entropy in order to formulate a general proof of the minimum energy principle as well as of other equivalent extremum principles that are valid for thermodynamic potentials and corresponding Massieu functions under different constraints. The current derivation aims at providing a coherent formal framework for such principles which may be also pedagogically useful as it fully exploits and highlights the equivalence between different schemes. We also elucidate the consequences of the extremum principles for the general shape of thermodynamic potentials in relation to first-order phase transitions.     

Entropy of three-dimensional BTZ black holes

~~Entropy of three-dimensional BTZ black holes~~     

Bosonic and Fermionic Entropy of (2 1)-Dimensional Charged Black Hole

From resolving Klein-Gordon equation and Dirac equation in (2 1)-dimensional charged black hole spacetime and using ‘t Hooft‘s boundary condition and “quasi-periodic“ boundary condition in the thin film brick wall model of black hole, which is introduced by LIU Weng-Biao and ZHAO Zheng, we obtain the bosonic and fermionic entropy of (2 1)-dimensional charged black hole, and find that the bosonic entropy is three times of fermionic entropy.     

Entropy of Dilatonic Black Hole

By using the method of quantum statistics, we directly derive the partition function of bosonic and fermionic field in dilatonic black hole and obtain the integral expression of the black hole's entropy, which avoids the difficulty in solving the wave equationof various particles. Then via the improved brick-wall method, membrane model, we obtain that we can choose proper parameter in order to let the thickness of film tend to zero and have it approach the surface of its horizon. Consequently the entropy of the black hole is proportional to the area of its horizon. In our result, the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. In the whole process, physics idea is clear; calculation is simple. We offer a new simple and direct way of calculating the entropy of different complicated black holes.     

Statistical Entropy of Black Cylinder

By using the method of quantum statistics, we directly derive the partition function of bosonic and fermionic fields in black cylinder. Then via the improved brick-wall method, membrane model, we obtain that if we choose the proper parameter, the entropy of black cylinder is proportional to the area of the horizon. In our result, the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. In the whole process, we do not take any approximation. We offer a new simple and direct way of calculating the entropy of different complicated black holes.     

Canonical Entropy of Reissner-Nordstrom Black Hole

Recently, Hawking radiation of the black hole has been studied using the tunnel effect method. It is found the radiation spectrum of the black hole is not a strictly pure thermal spectrum. How the departure from pure thermal spectrum affects the entropy? This is a very interesting problem. In this paper, we calculate the partition function by energy spectrum obtained by tunnel effect. Using the relation between the partition function and entropy, we derive the expression of entropy the general charged black hole. In our calculation, we not only consider the correction to the black hole entropy due to fluctuation of energy but also consider the effect of the change of the black hole charges on entropy. We discuss Reissner-Nordstrom black hole and obtain that Reissner-Nordstrom black hole cannot approach the extreme black hole by changing its charges.