The work illustrates the impossibility of decreasing entropy in a strictly random thermodynamic process in a non-isolated system using the example of heating a planet by solar radiation flux without and taking into ac...The work illustrates the impossibility of decreasing entropy in a strictly random thermodynamic process in a non-isolated system using the example of heating a planet by solar radiation flux without and taking into account its rotation around its own axis. That is, the second law of thermodynamics formulated for isolated systems continues to govern such systems. We have shown that in order to achieve a stationary state at lower values of temperature and entropy far from thermodynamic equilibrium at a maximum of temperature and entropy, it is necessary to have regular factors of nonrandom nature, one of which in this example is the rotation of the planet around its own axis. This means that the reason for the appearance of ordered structured objects in non-isolated thermodynamic systems is not the random process itself, but the action of dynamic control mechanisms, such as periodic external influences, nonlinear elements with positive feedback, catalysts for chemical reactions, etc. We present the plots with dependences of temperature and entropy versus time in non-isolated systems with purely random processes and in the presence of a control factor of non-random nature-rotation.展开更多
Based on the work of Ghosh and Pereze, who view the black hole entropy as the logarithm of the number of quantum states on the Quantum Isolated Horizon(QIH)§ the entropy of Reissner–Nordstr¨om black hole is...Based on the work of Ghosh and Pereze, who view the black hole entropy as the logarithm of the number of quantum states on the Quantum Isolated Horizon(QIH)§ the entropy of Reissner–Nordstr¨om black hole is studied.According to the Unruh temperature, the statistical entropy of quantum fields under the background of Reissner–Nordstr¨om spacetime is calculated by means of quantum statistics. In the calculations we take the integral from the position of QIH to infinity, so the obtained entropy is the entanglement entropy outside the QIH. In Reissner–Nordstr¨om spacetime it is shown that if only the position of QIH is properly chosen the leading term of logarithm of the number of quantum states on the QIH is equal to the leading term of the entanglement entropy outside the black hole horizon, and both are the Bekenstein–Hawking entropy. The results reveal the relation between the entanglement entropy of black hole and the logarithm of the number of quantum states.展开更多
In this paper, the BF theory method is applied to the nonrotating isolated horizons in Lovelock theory. The final entropy matches the Wald entropy formula for this theory. We also confirm the conclusion obtained by Bo...In this paper, the BF theory method is applied to the nonrotating isolated horizons in Lovelock theory. The final entropy matches the Wald entropy formula for this theory. We also confirm the conclusion obtained by Bodendorfer et al. that the entropy is related to the flux operator rather than the area operator in general diffeomorphic-invariant theory.展开更多
The quasi-local notion of an isolated horizon is employed to study the entropy of black holes without any particular symmetry in loop quantum gravity. The idea of characterizing the shape of a horizon by a sequence of...The quasi-local notion of an isolated horizon is employed to study the entropy of black holes without any particular symmetry in loop quantum gravity. The idea of characterizing the shape of a horizon by a sequence of local areas is successfully applied in the scheme to calculate the entropy by the S O(1, 1) BF boundary theory matching loop quantum gravity in the bulk. The generating function for calculating the microscopical degrees of freedom of a given isolated horizon is obtained. Numerical computations of small black holes indicate a new entropy formula containing the quantum correction related to the partition of the horizon. Further evidence shows that, for a given horizon area, the entropy decreases as a black hole deviates from the spherically symmetric one,and the entropy formula is also well suitable for big black holes.展开更多
文摘The work illustrates the impossibility of decreasing entropy in a strictly random thermodynamic process in a non-isolated system using the example of heating a planet by solar radiation flux without and taking into account its rotation around its own axis. That is, the second law of thermodynamics formulated for isolated systems continues to govern such systems. We have shown that in order to achieve a stationary state at lower values of temperature and entropy far from thermodynamic equilibrium at a maximum of temperature and entropy, it is necessary to have regular factors of nonrandom nature, one of which in this example is the rotation of the planet around its own axis. This means that the reason for the appearance of ordered structured objects in non-isolated thermodynamic systems is not the random process itself, but the action of dynamic control mechanisms, such as periodic external influences, nonlinear elements with positive feedback, catalysts for chemical reactions, etc. We present the plots with dependences of temperature and entropy versus time in non-isolated systems with purely random processes and in the presence of a control factor of non-random nature-rotation.
基金Supported by National Natural Science Foundation of Chinna under Grant Nos.11175109,11075098the doctoral Sustentation foundation of Shanxi Datong University(2011-B-03)
文摘Based on the work of Ghosh and Pereze, who view the black hole entropy as the logarithm of the number of quantum states on the Quantum Isolated Horizon(QIH)§ the entropy of Reissner–Nordstr¨om black hole is studied.According to the Unruh temperature, the statistical entropy of quantum fields under the background of Reissner–Nordstr¨om spacetime is calculated by means of quantum statistics. In the calculations we take the integral from the position of QIH to infinity, so the obtained entropy is the entanglement entropy outside the QIH. In Reissner–Nordstr¨om spacetime it is shown that if only the position of QIH is properly chosen the leading term of logarithm of the number of quantum states on the QIH is equal to the leading term of the entanglement entropy outside the black hole horizon, and both are the Bekenstein–Hawking entropy. The results reveal the relation between the entanglement entropy of black hole and the logarithm of the number of quantum states.
基金Supported by National Natural Science Foundation of China(11275207)
文摘In this paper, the BF theory method is applied to the nonrotating isolated horizons in Lovelock theory. The final entropy matches the Wald entropy formula for this theory. We also confirm the conclusion obtained by Bodendorfer et al. that the entropy is related to the flux operator rather than the area operator in general diffeomorphic-invariant theory.
基金supported by the National Natural Science Foundation of China (Grant Nos.11875006,and 11961131013)the support by the Polish Narodowe Centrum Nauki (Grant No.2018/30/Q/ST2/00811)。
文摘The quasi-local notion of an isolated horizon is employed to study the entropy of black holes without any particular symmetry in loop quantum gravity. The idea of characterizing the shape of a horizon by a sequence of local areas is successfully applied in the scheme to calculate the entropy by the S O(1, 1) BF boundary theory matching loop quantum gravity in the bulk. The generating function for calculating the microscopical degrees of freedom of a given isolated horizon is obtained. Numerical computations of small black holes indicate a new entropy formula containing the quantum correction related to the partition of the horizon. Further evidence shows that, for a given horizon area, the entropy decreases as a black hole deviates from the spherically symmetric one,and the entropy formula is also well suitable for big black holes.
