Effective first law of thermodynamics of black holes with two horizons

For a black hole with two horizons, the effective entropy is assumed to be a linear combination of the two entropies of the outer and inner horizons. In terms of the effective thermodynamic quantities the effective Bekenstein-Smarr formula and the effective first law of thermodynamics are derived.

Evaluating alternative hypotheses behind biodiversity and multifunctionality relationships in the forests of Northeastern China

Background:The importance of biodiversity in maintaining multiple ecosystem functions has been widely accepted.However,the specific mechanisms affecting biodiversity and ecosystem multifunctionality(BEMF)relationships in forests are largely unknown.This is particularly evident for the macroscale of a large forested landscape.Methods:Based on 412 one-tenth hectare field plots distributed over forested areas across northeastern China,we evaluated three alternative hypotheses explaining the relationships between BEMF,namely:niche complementarity,mass ratio,and vegetation quantity effect.We used Rao's quadratic entropy and community weighted mean trait values to quantify forest“biodiversity”.These two variables represent two complementary aspects of functional properties,which are in line with niche complementary and mass ratio effects,respectively.Results:Ecosystem multifunctionality was negatively associated with the community weighted mean values of acquisitive traits(a proxy of mass ratio effect).Rao's quadratic entropy(a proxy of niche complementarity)had no relationship with ecosystem multifunctionality.Higher stand biomass greatly increased ecosystem multifunctionality,which is in line with the vegetation quantity effect.Our results confirm that in the temperate forests of northeastern China,the relationship of BEMF was primarily affected by vegetation quantity,followed by mass ratio effects.Conclusions:The results of this study contribute to a better understanding of the main drivers of ecosystem multifunctionality in forest ecosystems.The results of this study provide additional evidence to support the vegetation quantity and mass ratio hypotheses in forest ecosystems.

Continuous phase transition of the de Sitter spacetime with charged black holes and cloud of strings and quintessence

Recently,some meaningful results have been obtained by studying the phase transition,critical exponents,and other thermodynamical properties of different black holes.Especially for the Anti-de Sitter(AdS)black holes,their thermodynamical properties nearby the critical point have attracted considerable attention.However,there exists little work on the thermodynamic properties of the de Sitter(dS)spacetime with black holes.In this paper,based on the effective thermodynamical quantities and the method of the Maxwell's equal-area law,we explore the phase equilibrium for the de Sitter spacetime with the charged black holes and the cloud of string and quintessence(i.e.,C-dSSQ spacetime).The boundaries of the two-phase coexistence region in both P_(eff)−T_(eff)and T_(eff)−S diagrams are obtained.The coexistent curve and the latent heat of phase transition for this system are also investigated.Furthermore,we analyze the effect of parameters(the state parameterωand the ratio of two horizon radii x=r+/r_(c))on the two-phase coexistence region boundary.The results indicate that the phase transition in C-dSSQ spacetime is analogous to that in a van der Waals fluid(vdw)system,which is determined by the electrical potential at the horizon.These results are helpful for understanding the basic properties of black holes and are also of great value for the establishment of quantum gravity.

Thermodynamics and phase transition of topological dS black holes with a nonlinear source

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.