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By use of the Jacobi determinant, we verify that, for a thermodynamic system which satisfies the first law of thermodynamics, if only there is second-order phase transition in the system, the Prigogine-Defay ratio is the constant 1. This conclusion is universal and independent of the concrete forms of the thermodynamic functions and also apply to black holes. [ABSTRACT FROM AUTHOR]

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein–Hawking entropy of a black hole. In this paper, we calculate the correction value of thermodynamic quantities of the Achucarro–Oritz black hole motivated by utilizing the generalized uncertainty principle. We obtain the Cardy–Verlinde formula after considering the correction. [ABSTRACT FROM AUTHOR]

Recently, there has been a lot of attention devoted to resolving the quantum corrections to the Bekenstein–Hawking entropy of the black hole. In particular, the coefficient of the logarithmic term in the black hole entropy correction has been of great interest. In this paper, the black hole is corresponded to a canonical ensemble in statistics by radiant spectrum, resulted from the black hole tunnelling effect studies and the partition function of ensemble is derived. Then the entropy of the black hole is calculated. When the first-order approximation is taken into account, the logarithmic term of entropy correction is consistent with the result of the generalized uncertainty principle. In our calculation, there are no uncertainty factors. The prefactor of the logarithmic correction and the one if fluctuation is considered are the same. Our result shows that if the thermal capacity is negative, there is no divergent term. We provide a general method for further discussion on quantum correction to Bekenstein–Hawking entropy. We also offer a theoretical basis for comparing string theory and loop quantum gravity and deciding which one is more reliable. [ABSTRACT FROM AUTHOR]

Starting from the Klein-Gordon equation, we calculate the entropy of Schwarzschild-de Sitter black hole in non-thermal-equilibrium by using the improved brick-wall methodmembrane model. When taking the proper cutoff in the obtained result, we obtain that both black hole's entropy and cosmic entropy are proportional to the areas of event horizon. We avoid the logarithmic term and stripped term in the original brick-wall method. It offers a new way of studying the entropy of the black hole in non-thermal-equilibrium. [ABSTRACT FROM AUTHOR]

On the basis of the first law of black hole thermodynamics, we propose the concept of effective temperature of de Sitter (dS) black holes and conjecture that the effective temperature should be the temperature of the dS black holes when the Hawking radiation temperatures of the black hole horizon and the cosmological horizon are equal. Choosing different independent variables, we can find a differential equation satisfied by the entropy of the dS black hole. It is shown that the differential equation of entropy is independent of the choice of independent variables. From the differential equation, we get the entropy of dS black hole and other effective thermodynamic quantities. We also discuss the influence of several parameters on the effective thermodynamic quantities. [ABSTRACT FROM AUTHOR]

Based on the works of Ghosh et al. who view the black hole entropy as the logarithm of the number of quantum states on the Quantum Isolated Horizon (QIH), the entropy of d-dimensional black hole is studied. According to the Unruh-Verlinde temperature deduced from the concept of entropic force, the statistical entropy of quantum fields under the background of d-dimensional spacetime is calculated by means of quantum statistics. The results reveal the relation between the entanglement entropy of black hole and the logarithm of the number of quantum states and display the effects of dimensions on the correction terms of the entanglement entropy. [ABSTRACT FROM AUTHOR]