In this study,we take the mass,electric charge,hair parameter,and cosmological constant of five-dimensional de Sitter hairy spacetime as the state parameters of the thermodynamic system,and when these state parameters...In this study,we take the mass,electric charge,hair parameter,and cosmological constant of five-dimensional de Sitter hairy spacetime as the state parameters of the thermodynamic system,and when these state parameters satisfy the first law of thermodynamics,the equivalent thermodynamic quantities of spacetime and the Smarr relation of five-dimensional de Sitter hairy spacetime are obtained.Then,we study the thermodynamic characteristics of the spacetime described by these equivalent thermodynamic quantities and find that de Sitter hairy spacetime has a phase transition and critical phenomena similar to those of van de Waals systems or charged AdS black holes.It is shown that the phase transition point of de Sitter hairy spacetime is determined by the ratio of two event horizon positions and the cosmic event horizon position.We discuss the influence of the hair parameter and electric charge on the critical point.We also find that the isochoric heat capacity of the spacetime is not zero,which is consistent with the ordinary thermodynamic system but differs from the isochoric heat capacity of AdS black holes,which is zero.Using the Ehrenfest equations,we prove that the critical phase transition is a second order equilibrium phase transition.Research on the thermodynamic properties of five-dimensional de Sitter hairy spacetime lays a foundation for finding a universal de Sitter spacetime thermodynamic system and studying its thermodynamic properties.Our universe is an asymptotically dS spacetime,and the thermodynamic characteristics of de Sitter hairy spacetime will help us understand the evolution of spacetime and provide a theoretical basis to explore the physical mechanism of the accelerated expansion of the universe.展开更多
Understanding the thermodynamic phase transition of black holes can provide a deep insight into the fundamental properties of black hole gravity to establish the theory of quantum gravity.We investigate the condition ...Understanding the thermodynamic phase transition of black holes can provide a deep insight into the fundamental properties of black hole gravity to establish the theory of quantum gravity.We investigate the condition and latent heat of phase transition for non-linear charged AdS black holes using Maxwell's equal-area law.In addition,we analyze the boundary and curve of the two-phase coexistence area in the expanded phase space.We suggest that the phase transition of the non-linear charged AdS black hole with the fixed temperature(T<T_(c))is related to the electric potential at the horizon,not only to the location of black hole horizon.Recently,the molecular number density was introduced to study the phase transition and microstructure of black holes.On this basis,we discuss the continuous phase transition of a non-linear charged AdS black hole to reveal the potential microstructure of a black hole by introducing the order parameter and using the scalar curvature.展开更多
From a new perspective, we discuss the thermodynamic entropy of (n+2)-dimensional Reissner-Nordstrmde Sitter (RNdS) black hole and analyze the phase transition of the effective thermodynamic system. Considering the co...From a new perspective, we discuss the thermodynamic entropy of (n+2)-dimensional Reissner-Nordstrmde Sitter (RNdS) black hole and analyze the phase transition of the effective thermodynamic system. Considering the correlations between the black hole event horizon and the cosmological horizon, we conjecture that the total entropy of the RNdS black hole should contain an extra term besides the sum of the entropies of the two horizons. In the lukewarm case, the effective temperature of the RNdS black hole is the same as that of the black hole horizon and the cosmological horizon. Under this condition, we obtain the extra contribution to the total entropy. With the corrected entropy, we derive other effective thermodynamic quantities and analyze the phase transition of the RNdS black hole in analogy to the usual thermodynamic system.展开更多
We discuss black hole solutions of Einstein-Λ gravity in the presence of nonlinear electrodynamics in dS spacetime.Considering the correlation of the thermodynamic quantities respectively corresponding to the black h...We discuss black hole solutions of Einstein-Λ gravity in the presence of nonlinear electrodynamics in dS spacetime.Considering the correlation of the thermodynamic quantities respectively corresponding to the black hole horizon and cosmological horizon of dS spacetime and taking the region between the two horizons as a thermodynamic system,we derive effective thermodynamic quantities of the system according to the first law of thermodynamics,and investigate the thermodynamic properties of the system under the influence of nonlinearity parameter α.It is shown that nonlinearity parameter α influences the position of the black hole horizon and the critical state of the system,and along with electric charge has an effect on the phase structure of the system,which is obvious,especially as the effective temperature is below the critical temperature.The critical phase transition is proved to be second-order equilibrium phase transition by using the Gibbs free energy criterion and Ehrenfest equations.展开更多
The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole ...The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.展开更多
We examine the conditions under which descriptive inference can be based directly on theobserved distribution in a non-probability sample, under both the super-population and quasirandomisation modelling approaches. R...We examine the conditions under which descriptive inference can be based directly on theobserved distribution in a non-probability sample, under both the super-population and quasirandomisation modelling approaches. Review of existing estimation methods reveals that thetraditional formulation of these conditions may be inadequate due to potential issues of undercoverage or heterogeneous mean beyond the assumed model. We formulate unifying conditions that are applicable to both types of modelling approaches. The difficulties of empiricallyvalidating the required conditions are discussed, as well as valid inference approaches usingsupplementary probability sampling. The key message is that probability sampling may still benecessary in some situations, in order to ensure the validity of descriptive inference, but it can bemuch less resource-demanding given the presence of a big non-probability sample.展开更多
Understanding the thermodynamic phase transition of black holes can provide deep insights into the fundamental properties of black hole gravity and help to establish quantum gravity.In this work,we investigate the pha...Understanding the thermodynamic phase transition of black holes can provide deep insights into the fundamental properties of black hole gravity and help to establish quantum gravity.In this work,we investigate the phase transition and its dynamics for the charged EPYM AdS black hole.Through reconstructing Maxwell's equal-area law,we find there exists a high-/low-potential black hole(HPBH/LPBL)phase transition,not only the pure large/small black hole phase transition.The Gibbs free energy landscape(G_(L))is treated as a function of the black hole horizon,which is the order parameter of the phase transition due to thermal fluctuation.From the viewpoint of G_(L),the stable HPBH/LPBL states correspond to two wells of G_(L),which have the same depth.The unstable intermediate-potential black hole state corresponds to the local maximum of G_(L).Then we focus on the probability evolution governed by the Fokker-Planck equation.Through solving the Fokker-Planck equation with different reflection/absorption boundary conditions and initial conditions,the dynamics of switching between the coexistent HPBH and LPBL phases is probed within the first passage time.Furthermore,the effect of temperature on the dynamic properties of the phase transition is also investigated.展开更多
In this paper,we consider(n+1)-dimensional topological dilaton de Sitter black holes with a powerMaxwell field as thermodynamic systems.The thermodynamic quantities corresponding to the black hole horizon and the cosm...In this paper,we consider(n+1)-dimensional topological dilaton de Sitter black holes with a powerMaxwell field as thermodynamic systems.The thermodynamic quantities corresponding to the black hole horizon and the cosmological horizon are interrelated.Therefore,the total entropy of the space-time should be the sum of the entropies of the black hole horizon and the cosmological horizon plus a correction term which is produced by the association of the two horizons.We analyze the entropic force produced by the correction term at given temperatures,which is affected by the parameters and dimensions of the space-time.It is shown that the change of entropic force with the position ratio of the two horizons in some regions is similar to that of the variation of the Lennard-Jones force with the position of particles.If the effect of entropic force is similar to that of the Lennard-Jones force,and other forces are absent,the motion of the cosmological horizon relative to the black hole horizon should have an oscillating process.The entropic force between the two horizons is probably one of the participants in driving the evolution of the universe.展开更多
基金the National Natural Science Foundation of China(12075143)。
文摘In this study,we take the mass,electric charge,hair parameter,and cosmological constant of five-dimensional de Sitter hairy spacetime as the state parameters of the thermodynamic system,and when these state parameters satisfy the first law of thermodynamics,the equivalent thermodynamic quantities of spacetime and the Smarr relation of five-dimensional de Sitter hairy spacetime are obtained.Then,we study the thermodynamic characteristics of the spacetime described by these equivalent thermodynamic quantities and find that de Sitter hairy spacetime has a phase transition and critical phenomena similar to those of van de Waals systems or charged AdS black holes.It is shown that the phase transition point of de Sitter hairy spacetime is determined by the ratio of two event horizon positions and the cosmic event horizon position.We discuss the influence of the hair parameter and electric charge on the critical point.We also find that the isochoric heat capacity of the spacetime is not zero,which is consistent with the ordinary thermodynamic system but differs from the isochoric heat capacity of AdS black holes,which is zero.Using the Ehrenfest equations,we prove that the critical phase transition is a second order equilibrium phase transition.Research on the thermodynamic properties of five-dimensional de Sitter hairy spacetime lays a foundation for finding a universal de Sitter spacetime thermodynamic system and studying its thermodynamic properties.Our universe is an asymptotically dS spacetime,and the thermodynamic characteristics of de Sitter hairy spacetime will help us understand the evolution of spacetime and provide a theoretical basis to explore the physical mechanism of the accelerated expansion of the universe.
基金the Natural Science Foundation of China(11705106,11475108,12075143)the Natural Science Foundation of Shanxi Province,China(201901D111315)+2 种基金the Natural Science Foundation for Young Scientists of Shanxi Province,China(201901D211441)the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province(2020L0471,2020L0472)the Science Technology Plan Project of Datong City,China(2020153)。
文摘Understanding the thermodynamic phase transition of black holes can provide a deep insight into the fundamental properties of black hole gravity to establish the theory of quantum gravity.We investigate the condition and latent heat of phase transition for non-linear charged AdS black holes using Maxwell's equal-area law.In addition,we analyze the boundary and curve of the two-phase coexistence area in the expanded phase space.We suggest that the phase transition of the non-linear charged AdS black hole with the fixed temperature(T<T_(c))is related to the electric potential at the horizon,not only to the location of black hole horizon.Recently,the molecular number density was introduced to study the phase transition and microstructure of black holes.On this basis,we discuss the continuous phase transition of a non-linear charged AdS black hole to reveal the potential microstructure of a black hole by introducing the order parameter and using the scalar curvature.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11475108
文摘From a new perspective, we discuss the thermodynamic entropy of (n+2)-dimensional Reissner-Nordstrmde Sitter (RNdS) black hole and analyze the phase transition of the effective thermodynamic system. Considering the correlations between the black hole event horizon and the cosmological horizon, we conjecture that the total entropy of the RNdS black hole should contain an extra term besides the sum of the entropies of the two horizons. In the lukewarm case, the effective temperature of the RNdS black hole is the same as that of the black hole horizon and the cosmological horizon. Under this condition, we obtain the extra contribution to the total entropy. With the corrected entropy, we derive other effective thermodynamic quantities and analyze the phase transition of the RNdS black hole in analogy to the usual thermodynamic system.
基金supported by NSFC under Grant No.11705107by the doctoral Sustentation Fund of Shanxi Datong University(2015-B-10).
文摘We discuss black hole solutions of Einstein-Λ gravity in the presence of nonlinear electrodynamics in dS spacetime.Considering the correlation of the thermodynamic quantities respectively corresponding to the black hole horizon and cosmological horizon of dS spacetime and taking the region between the two horizons as a thermodynamic system,we derive effective thermodynamic quantities of the system according to the first law of thermodynamics,and investigate the thermodynamic properties of the system under the influence of nonlinearity parameter α.It is shown that nonlinearity parameter α influences the position of the black hole horizon and the critical state of the system,and along with electric charge has an effect on the phase structure of the system,which is obvious,especially as the effective temperature is below the critical temperature.The critical phase transition is proved to be second-order equilibrium phase transition by using the Gibbs free energy criterion and Ehrenfest equations.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.11205097)in part by the National Natural Science Foundation of China(Grant No.11475108)+1 种基金supported by Program for the Natural Science Foundation of Shanxi Province,China(Grant No.201901D111315)the Natural Science Foundation for Young Scientists of Shanxi Province,China(Grant No.201901D211441)。
文摘The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.
文摘We examine the conditions under which descriptive inference can be based directly on theobserved distribution in a non-probability sample, under both the super-population and quasirandomisation modelling approaches. Review of existing estimation methods reveals that thetraditional formulation of these conditions may be inadequate due to potential issues of undercoverage or heterogeneous mean beyond the assumed model. We formulate unifying conditions that are applicable to both types of modelling approaches. The difficulties of empiricallyvalidating the required conditions are discussed, as well as valid inference approaches usingsupplementary probability sampling. The key message is that probability sampling may still benecessary in some situations, in order to ensure the validity of descriptive inference, but it can bemuch less resource-demanding given the presence of a big non-probability sample.
基金Supported by the National Natural Science Foundation of China(11705106,11475107,12075143)the Natural Science Foundation of Shanxi Province,China(201901D111315)+2 种基金the Natural Science Foundation for Young Scientists of Shanxi Province,China(201901D211441)the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province(2020L0471,2020L0472,2016173)the Science Technology Plan Project of Datong City,China(2020153)。
文摘Understanding the thermodynamic phase transition of black holes can provide deep insights into the fundamental properties of black hole gravity and help to establish quantum gravity.In this work,we investigate the phase transition and its dynamics for the charged EPYM AdS black hole.Through reconstructing Maxwell's equal-area law,we find there exists a high-/low-potential black hole(HPBH/LPBL)phase transition,not only the pure large/small black hole phase transition.The Gibbs free energy landscape(G_(L))is treated as a function of the black hole horizon,which is the order parameter of the phase transition due to thermal fluctuation.From the viewpoint of G_(L),the stable HPBH/LPBL states correspond to two wells of G_(L),which have the same depth.The unstable intermediate-potential black hole state corresponds to the local maximum of G_(L).Then we focus on the probability evolution governed by the Fokker-Planck equation.Through solving the Fokker-Planck equation with different reflection/absorption boundary conditions and initial conditions,the dynamics of switching between the coexistent HPBH and LPBL phases is probed within the first passage time.Furthermore,the effect of temperature on the dynamic properties of the phase transition is also investigated.
基金Supported by the National Natural Science Foundation of China(11705107,11847123,11475108,11705106,11605107)the Natural Science Foundation of Shanxi Province,China(201601D102004)the Scientific and Technological Innovation Programs of Higher Education Institutions of Shanxi Province,China(2019L0743,2020L0471,2020L0472)。
文摘In this paper,we consider(n+1)-dimensional topological dilaton de Sitter black holes with a powerMaxwell field as thermodynamic systems.The thermodynamic quantities corresponding to the black hole horizon and the cosmological horizon are interrelated.Therefore,the total entropy of the space-time should be the sum of the entropies of the black hole horizon and the cosmological horizon plus a correction term which is produced by the association of the two horizons.We analyze the entropic force produced by the correction term at given temperatures,which is affected by the parameters and dimensions of the space-time.It is shown that the change of entropic force with the position ratio of the two horizons in some regions is similar to that of the variation of the Lennard-Jones force with the position of particles.If the effect of entropic force is similar to that of the Lennard-Jones force,and other forces are absent,the motion of the cosmological horizon relative to the black hole horizon should have an oscillating process.The entropic force between the two horizons is probably one of the participants in driving the evolution of the universe.
